##### Question 1:

Find the perfect square numbers between:

30 and 40

##### Answer:

Perfect square number between 30 and 40 is 36.

##### Question 2:

Find the perfect square numbers between:

50 and 60

##### Answer:

There is no perfect square number between 50 and 60.

##### Question 3:

Can we say whether the following number is a perfect square? How do we know?

1057

##### Answer:

1057

1057 has 7 at its unit’s digit.

$\therefore $ 1057 is not a perfect square.

##### Question 4:

Can we say whether the following number is a perfect square? How do we know?

23453

##### Answer:

23453

23453 has 3 at its unit’s digit.

$\therefore $ 23453 is not a perfect square.

##### Question 5:

Can we say whether the following number is a perfect square? How do we know?

7928

##### Answer:

7928

7928 has 8 at its unit’s digit.

$\therefore $ 7928 is not a perfect square.

##### Question 6:

Can we say whether the following number is a perfect square? How do we know?

222222

##### Answer:

222222

222222 has 2 at its unit’s digit

$\therefore $ 222222 is not a perfect square,

##### Question 7:

Can we say whether the following number is a perfect square? How do we know?

1069

##### Answer:

1069 has 9 at its unit’s digit

$\therefore $ 1069 is can be a perfect square.

##### Question 8:

Can we say whether the following number is a perfect square? How do we know?

2061

##### Answer:

2061 has 1 at its unit’s digit

$\therefore $ 2061 is can be a perfect square.

##### Question 9:

Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.

##### Answer:

217, 168, 90, 4000, 143 etc.

##### Question 10:

Write five numbers which you cannot decide just by looking at their unit’s digit (or one’s place) whether they are square numbers or not.

##### Answer:

91, 79, 169, 245, 40005 etc.

##### Question 11:

Which of (123)^{2}, (77)^{2}, (82)^{2}, (161)^{2}, (109)^{2}.

Which would end with digit 1?

##### Answer:

(123)^{2} = 15129

(77)^{2} = 5929

(82)^{2} = 6724

(161)^{2} = 25921

(109)^{2} = 11881

Thus, (161)^{2} and (109)^{2} ends with digit 1.

##### Question 12:

Which of the following numbers would have digit 6 at unit’s place?

19^{2}

##### Answer:

19^{2} = 361

Unit’s digit = 1

##### Question 13:

Which of the following number would have digit 6 at unit’s place?

24^{2}

##### Answer:

24^{2} = 576

Unit’s digit = 6

##### Question 14:

Which of the following number would have digit 6 at unit’s place?

26^{2}

##### Answer:

26^{2} = 676

Unit’s digit = 6

##### Question 15:

Which of the following number would have digit 6 at unit’s place?

36^{2}

##### Answer:

36^{2} = 1296

Unit’s digit = 6

##### Question 16:

Which of the following number would have digit 6 at unit’s place?

34^{2}

##### Answer:

34^{2} = 1156

Unit’s digit = 6.

Thus, 24^{2} , 26^{2} , 36^{2} and 34^{2} have digit 6 at units place.

##### Question 17:

What will be the ‘‘one’s digit’’ in the square of the following number?

1234

##### Answer:

1234

Unit’s digit = 4

$\therefore $ Unit’s digit of square = (4)^{2}

= 16 i.e., 6.

##### Question 18:

What will be the ‘‘one’s digit’’ in the square of the following number?

26387

##### Answer:

26387

Unit’s digit = 7

$\therefore $ Unit’s digit of square = (7)^{2}

= 49 i.e., 9.

##### Question 19:

What will be the ‘‘one’s digit’’ in the square of the following number?

52698

##### Answer:

52698

Unit’s digit = 8

$\therefore $ Unit’s digit of square = (8)^{2} = 64 i.e., 4

##### Question 20:

What will be the ‘‘one’s digit’’ in the square of the following number?

99880

##### Answer:

99880

Unit’s digit = 0

$\therefore $ Unit’s digit of square = 0.

##### Question 21:

What will be the ‘‘one’s digit’’ in the square of the following number?

21222

##### Answer:

21222

Unit’s digit = 2

$\therefore $ Unit’s digit of square = (2)^{2} = 4.

##### Question 22:

What will be the ‘‘one’s digit’’ in the square of the following number?

9106

##### Answer:

9106

Unit’s digit = 6

$\therefore $ Unit’s digit of square = (6)^{2} = 36 i.e., 6.

##### Question 23:

The square of which of the following would be an odd number/an even number?

Why?

727

##### Answer:

727

As the number 727 is an odd number.

$\therefore $ Its square is also an odd number.

##### Question 24:

The square of which of the following would be an odd number/an even number?

Why?

158

##### Answer:

158

As 158 is an even number.

$\therefore $ Its square is also an even number.

##### Question 25:

The square of which of the following would be an odd number/an even number?

Why?

269

##### Answer:

269

As 269 is an odd number.

$\therefore $ Its square is also an odd number.

##### Question 26:

The square of which of the following would be an odd number/an even number?

Why?

1980

##### Answer:

1980

As 1980 has 0 as its unit’s digit and is an
even number.

$\therefore $ Its square also has its unit’s digit as 0
and is an even number.

##### Question 27:

What will be the number of zeroes in the
square of the following number?

60

##### Answer:

(60)^{2} = 3600

$\therefore $ Number of zeroes = 2.

##### Question 28:

What will be the number of zeroes in the
square of the following number?

400

##### Answer:

(400)^{2} = 160000

$\therefore $ Number of zeroes = 4.

##### Question 29:

How many natural numbers lies between

9^{2} and 10^{2}? Between 11^{2} and 12^{2}?

##### Answer:

In general, there are 2n natural numbers
between the squares of the numbers n and
(n + 1).

i.e., Between (9)^{2} and (9 + 1)^{2} = (10)^{2}

There are 2n i.e. 2 (9) = (18) natural numbers.

i.e., 9^{2} = 81

and 10^{2}= 100

(81), 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,
94, 95, 96, 97, 98, 99, (100).

There are 2n i.e. 2 (11) = 22 natural numbers.

i.e., (11)^{2} = 121

and (12)^{2} = 144

(121), 122, 123, 124, 125, 126, 127, 128, 129, 130,
131, 132, 133, 134, 135, 136, 137, 138, 139, 140,
141, 142, 143, (144).

##### Question 30:

How many non-square numbers lie between the following pairs of numbers.

(100)^{2} and (101)^{2}.

##### Answer:

In general; there are 2n non-square numbers
lies between the squares of the numbers n and
(n + 1).

Between (100)^{2} and (100 + 1)^{2} = (101)^{2}.

There are; 2n = 2 (100) = 200 non-square numbers

##### Question 31:

How many non-square numbers lie between the following pairs of numbers.

(90)^{2} and (91)^{2}.

##### Answer:

Between (90)^{2} and (90 + 1)^{2} = (91)^{2}.

There are, 2n = 2 (90) = 180 non-square numbers.

##### Question 32:

How many non-square numbers lie between the following pairs of numbers.

(1000)^{2} and (1001)^{2}.

##### Answer:

Between (1000)^{2} and (1001)^{2}.

There are, 2n = 2 (1000) = 2000 non-square numbers.

##### Question 33:

Find whether each of the following numbers is a perfect square or not.

121

##### Answer:

Note. Sum of first n odd natural numbers is n^{2}.

i.e. If a number is a square number, it has to be the sum of consecutive odd numbers starting from 1.

(i) 121

$\therefore $ 121 - 1 = 120

120 - 3 = 117

117 - 5 = 112

112 - 7 = 105

105 - 9 = 96

96 - 11 = 85

85 - 13 = 72

72 - 15 = 57

57 - 17 = 40

40 - 19 = 21

21 - 21 = 0

$\therefore $ 121 is a perfect square number.

##### Question 34:

Find whether each of the following numbers is a perfect square or not.

55

##### Answer:

55

$\therefore $ 55 - 1 = 54

54 - 3 = 51

51 - 5 = 46

46 - 7 = 39

39 - 9 = 30

30 - 11 = 19

19 - 13 = 6

6 - 15 = - 9

$\therefore $ 55 is not a perfect square number.

##### Question 35:

Find whether each of the following numbers is a perfect square or not.

81

##### Answer:

81

81 - 1 = 80

80 - 3 = 77

77 - 5 = 72

72 - 7 = 65

65 - 9 = 56

56 - 11 = 45

45 - 13 = 32

32 - 15 = 17

17 - 17 = 0

$\therefore $ 81 is a perfect square number.

##### Question 36:

Find whether each of the following numbers is a perfect square or not.

49

##### Answer:

49

$\therefore $ 49 - 1 = 48

48 - 3 = 45

45 - 5 = 40

40 -7 = 33

33 - 9 = 24

24 - 11 = 13

13 - 13 = 0

$\therefore $ 49 is a perfect square number.

##### Question 37:

Find whether each of the following numbers is a perfect square or not.

69

##### Answer:

69

$\therefore $ 69 - 1 = 68

68 - 3 = 65

65 - 5 = 60

60 - 7 = 53

53 - 9 = 44

44 - 11 = 33

33 - 13 = 20

20 - 15 = 5

5 - 17 = - 12

$\therefore $ 69 is not a perfect square number.

##### Question 38:

Express the following as the sum of two consecutive integers.

(i) (21)^{2}

(ii) (13)^{2}

(iii) (11)^{2}

((iv)) (19) ^{2}

##### Answer:

(i) (21)^{2} = 441 = 220 + 221

(ii) (13)^{2} = 169 = 84 + 85

(iii) (11)^{2} = 121 = 60 + 61

(iv) (19)^{2} = 361 = 180 + 181

##### Question 39:

Write the square making use of pattern:

111111^{2}

##### Answer:

111111^{2} = 1 2 3 4 5 6 5 4 3 2 1

##### Question 40:

Write the square making use of pattern:

1111111^{2}

##### Answer:

1111111^{2} = 1 2 3 4 5 6 7 6 5 4 3 2 1

##### Question 41:

Can you find the square of the following number using pattern:

6666667^{2}

##### Answer:

6666667^{2} = 4 4 4 4 4 4 4 8 8 8 8 8 8 9

##### Question 42:

Can you find the square of the following number using pattern:

66666667^{2}

##### Answer:

66666667^{2} = 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 9

##### Question 43:

What will be the unit digit of the squares of the following number:

81

##### Answer:

81

The unit digit of 81 = 1

$\therefore $ The unit digit of (81)^{2} is (1)^{2} = 1

##### Question 44:

What will be the unit digit of the squares of the following numbers:

272

##### Answer:

272

The unit digit of 272 = 2

$\therefore $ The unit digit of (272)^{2} is (2)^{2} = 4

##### Question 45:

What will be the unit digit of the squares of the following number:

799

##### Answer:

799

The unit digit of 799 = 9

$\therefore $ The unit digit of (799)^{2} is (9)^{2} = 81

i.e., 1.

##### Question 46:

What will be the unit digit of the squares of the following number:

3853

##### Answer:

3853

The unit digit of 3853 = 3

$\therefore $ The unit digit of (3853)^{2} is (3)^{2} = 9.

##### Question 47:

What will be the unit digit of the squares of the following number:

1234

##### Answer:

1234

The unit digit of 1234 = 4

$\therefore $ The unit digit of (1234)^{2} is (4)^{2} = 16

i.e., 6.

##### Question 48:

What will be the unit digit of the squares of the following numbers:

26387

##### Answer:

26387

The unit digit of 26387 = 7

$\therefore $ The unit digit of (26387)^{2} is (7)^{2} = 49

i.e., 9.

##### Question 49:

What will be the unit digit of the squares of the following number:

52698

##### Answer:

52698

The unit digit of 52698 = 8

$\therefore $ The unit digit of (52698)^{2} is (8)^{2} = 64

i.e., 4.

##### Question 50:

What will be the unit digit of the squares of the following number:

99880

##### Answer:

99880

The unit digit of 99880 = 0

$\therefore $ The unit digit of (99880)^{2} is (0)^{2} = 0.

##### Question 51:

What will be the unit digit of the squares of the following number:

12796

##### Answer:

12796

The unit digit of 12796 = 6

$\therefore $ The unit digit of (12796)^{2} is (6)^{2} = 36

i.e., 6.

##### Question 52:

What will be the unit digit of the squares of the following number:

55555

##### Answer:

55555

The unit digit of 55555 = 5

$\therefore $ The unit digit of (55555)^{2} is (5)^{2} = 25

i.e., 5

##### Question 53:

The following numbers are obviously not
perfect squares. Give reason.

(i) 1057 (ii) 23453 (iii) 7928

(iv) 222222 (v) 64000 (vi) 89722

(vii) 222000 (viii) 505050.

##### Answer:

The numbers 1057, 23453, 7928, 222222 and 89722 are not perfect squares, because, a number ending in 2, 3, 7 or 8 is never a perfect square. Also 64000, 222000 and 505050 cannot be perfect squares as they end with odd number of zeros.

##### Question 54:

The squares of which of the following
would be odd numbers?

(i) 431 (ii) 2826

(iii) 7779 (iv) 82004

##### Answer:

(i) 431 and (iii) 7779 are odd numbers,
therefore, the squares of these numbers
are also odd numbers.

‘‘Because the square of an odd number is always
an odd number.’’

##### Question 55:

Observe the following pattern and find the
missing digits:

11^{2} = 121

101^{2} = 10201

1001^{2} = 1002001

100001^{2} = 1............2.........1

1000000^{1} = .................

##### Answer:

11^{2} = 121

101^{2} = 10201

1001^{2} = 1002001

100001^{2} = 10000200001

10000001^{2} = 100000020000001

##### Question 56:

Observe the following pattern and supply
the missing numbers:

11^{2} = 121

101^{2} = 10201

10101^{2} = 102030201

1010101^{2} = .............

.............^{2} = 10203040504030201

##### Answer:

11^{2} = 121

101^{2} = 10201

10101^{2} = 102030201

1010101^{2} = 1020304030201

101010101^{2} = 10203040504030201

##### Question 57:

Using the given pattern, find the missing
numbers.

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2}+ 12^{2} = 13^{2}

4^{2} + 5^{2} + .............^{2} = 21^{2}

5^{2} + ...^{2} + 30^{2} = 31^{2}

6^{2} +7^{2} + .............^{2} = ...^{2}

##### Answer:

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2} + 12^{2} = 13^{2}

4^{2} + 5^{2} + 20^{2} = 21^{2}

5^{2} + 6^{2} + 30^{2} = 31^{2}

6^{2} + 7^{2} + 42^{2} = 43^{2}

##### Question 58:

Without adding, find the sum:

1 + 3 + 5 + 7 + 9

##### Answer:

We have,

1 + 3 + 5 + 7 + 9

= Sum of first 5 odd numbers.

= (5)^{2} = 25

##### Question 59:

Without adding, find the sum:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

##### Answer:

We have:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

= Sum of first 10 odd numbers

= (10)^{2} = 100

##### Question 60:

Without adding, find the sum:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23.

##### Answer:

We have:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

= Sum of first 12 odd numbers

= (12)^{2} = 144

##### Question 61:

Express 49 as the sum of 7 odd numbers.

##### Answer:

49 = 1 + 3 + 5 + 7 + 9 + 11 + 13.

##### Question 62:

Express 121 as the sum of 11 odd numbers

##### Answer:

121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21.

##### Question 63:

How many numbers lie between squares of the following numbers?

12 and 13

##### Answer:

Between (12)^{2} and (12 + 1)^{2} = (13)^{2}.

There are, 2n = 2(12) = 24 natural numbers.

##### Question 64:

How many numbers lie between squares of the following numbers?

25 and 26

##### Answer:

Between (25)^{2} and (25 + 1)^{2} = (26)^{2}

There are, 2n = 2(25) = 50 natural numbers.

##### Question 65:

How many numbers lie between squares of the following numbers?

99 and 100.

##### Answer:

Between (99)^{2} and (99 + 1)^{2} = (100)^{2}.

There are, 2n = 2(99) = 198 natural numbers.

##### Question 66:

Find the squares of the following number containing 5 in unit’s place.

15

##### Answer:

(15)^{2} = (1 × 2) hundreds + 25

= 200 + 25 = 225

##### Question 67:

Find the squares of the following number containing 5 in unit’s place.

95

##### Answer:

(95)^{2} = (9 × 10) hundreds + 25

= 9000 + 25 = 9025

##### Question 68:

Find the squares of the following number containing 5 in unit’s place.

105

##### Answer:

(105)^{2} = (10 × 11) hundreds + 25

= 11000 + 25 = 11025

##### Question 69:

Find the squares of the following number containing 5 in unit’s place.

205

##### Answer:

(205)^{2} = (20 × 21) hundreds + 25

= 42000 + 25 = 42025

##### Question 70:

Find the square of the following numbers:

32

##### Answer:

(32)^{2} = (30 + 2)^{2} = (30 + 2)(30 + 2)

= 30(30 + 2) + 2(30 + 2)

= 30^{2} + 30 × 2 + 2 × 30 + 2^{2}

= 900 + 60 + 60 + 4

= 1024

##### Question 71:

Find the square of the following numbers:

35

##### Answer:

(35)^{2} = (30 + 5)^{2}

= (30 + 5)(30 + 5)

= 30(30 + 5) + 5(30 + 5)

= 30^{2} + 30 × 5 + 5 × 30 +5^{2}

= 900 + 150 + 150 + 25

= 1225

##### Question 72:

Find the square of the following numbers:

86

##### Answer:

(86)^{2} = (80 + 6)^{2}

= (80 + 6)(80 + 6)

= 80(80 + 6) + 6(80 + 6)

= 80^{2} + 80 × 6 + 6 × 80 + 6^{2}

= 6400 + 480 + 480 + 36

= 7396

##### Question 73:

Find the square of the following numbers:

93

##### Answer:

(93)^{2} = (90 + 3)^{2}

= (90 + 3)(90 + 3)

= 90(90 + 3) + 3(90 + 3)

= 90^{2} + 90 × 3 + 3 × 90 + 3^{2}

= 8100 + 270 + 270 + 9

= 8649

##### Question 74:

Find the square of the following numbers:

71

##### Answer:

(71)^{2} = (70 + 1)^{2}

= (70 + 1)(70 + 1)

= 70(70 + 1) + 1(70 + 1)

= 70^{2} + 70 × 1 + 1 × 70 + 1^{2}

= 4900 + 70 + 70 + 1

= 5041

##### Question 75:

Find the square of the following numbers:

46.

##### Answer:

(46)^{2} = (40 + 6)^{2}

= (40 + 6) (40 + 6)

= 40(40 + 6) + 6(40 + 6)

= 40^{2} + 40 × 6 + 6 × 40 + 6^{2}

= 1600 + 240 + 240 + 36

= 2116

##### Question 76:

Write a Pythagorean Triplet whose one member is:

6

##### Answer:

##### Question 77:

Write a Pythagorean Triplet whose one member is:

14

##### Answer:

##### Question 78:

Write a Pythagorean Triplet whose one member is:

16

##### Answer:

##### Question 79:

Write a Pythagorean Triplet whose one member is:

18.

##### Answer:

##### Question 80:

(i) 11^{2}= 121. What is the square root of 121.

(ii) 14^{2} = 196. What is the square root of 196.

##### Answer:

(i) 11^{2} = 121; therefore, square root of 121 is 11.

(ii) 14^{2} = 196; therefore, square root of 196 is 14.

##### Question 81:

(-1)^{2} = 1. Is -1 a square root of 1?

##### Answer:

Yes, since (1)^{2} = 1 and (-1)^{2} = 1

So, we can say that square root of 1 is 1 and -1.

##### Question 82:

(-2)^{2} = 4. Is -2, a square root of 4?

##### Answer:

Yes, square root of 4 is -2.

##### Question 83:

(-9)^{2} = 81. Is -9, a square root of 81?

##### Answer:

Yes, -9 is a square root of 81.

##### Question 84:

By repeated subtraction of odd numbers from 1, find whether the 121 is perfect squares or not? If the number is a perfect square, then, find its square root.

##### Answer:

121

$\therefore $ (i) 121 - 1 = 120 (ii) 120 - 3 = 117

(iii) 117 - 5 = 112 (iv) 112 - 7 = 105

(v) 105 - 9 = 96 (vi) 96 - 11 = 85

(vii) 85 - 13 = 72 (viii) 72 - 15 = 57

(ix) 57 - 17 = 40 (x) 40 - 19 = 21

(xi) 21 - 21 = 0

Here, we get 0 at 11^{th} step.

##### Question 85:

By repeated subtraction of odd numbers from 1, find whether the 55 is perfect squares or not? If the number is a perfect square, then, find its square root.

##### Answer:

55

(i) 55 - 1 = 54 (ii) 54 - 3 = 51

(iii) 51 - 5 = 46 (iv) 46 - 7 = 39

(v) 39 - 9 = 30 (vi) 30 - 11 = 19

(vii) 19 - 13 = 6 (viii) 6 - 15 = - 9

Here, 0 is not obtained after repeated

subtraction.

$\therefore $ 55 is not a perfect square.

##### Question 86:

By repeated subtraction of odd numbers from 1, find whether the 36 is perfect squares or not? If the number is a perfect square, then, find its square root.

##### Answer:

36

(i) 36 - 1 = 35 (ii) 35 - 3 = 32

(iii) 32 - 5 = 27 (iv) 27 - 7 = 20

(v) 20 - 9 = 11 (vi) 11 - 11 = 0

Here, we get 0 at 6^{th} step.

##### Question 87:

By repeated subtraction of odd numbers from 1, find whether the 49 is perfect squares or not? If the number is a perfect square, then, find its square root.

##### Answer:

49

(i) 49 - 1 = 48 (ii) 48 - 3 = 45

(iii) 45 - 5 = 40 (iv) 40 - 7 = 33

(v) 33 - 9 = 24 (vi) 24 - 11 = 13

(vii) 13 - 13 = 0

Here, we get 0 at 7^{th} step.

##### Question 88:

By repeated subtraction of odd numbers from 1, find whether the 90 is perfect squares or not? If the number is a perfect square, then, find its square root.

##### Answer:

90

(i) 90 - 1 = 89 (ii) 89 - 3 = 86

(iii) 86 - 5 = 81 (iv) 81 - 7 = 74

(v) 74 - 9 = 65 (vi) 65 - 11 = 54

(vii) 54 - 13 = 41 (viii) 41 - 15 = 26

(ix) 26 - 17 = 9 (x) 9 - 19 = -10

Here, 0 is not obtained after 10^{th} step.

$\therefore $ 90 is not a perfect square.

##### Question 89:

What could be the ‘one’s’ digits of the square

root of each of the following numbers?

(i) 9801 (ii) 99856

(iii) 998001 (iv) 657666025.

##### Answer:

##### Question 90:

Without doing any calculation, find the numbers which are surely not perfect squares.

(i) 153 (ii) 257

(iii) 408 (iv) 441.

##### Answer:

##### Question 91:

Find the square roots of 100 and 169 by the method of repeated subtraction.

##### Answer:

(a) 100

(i) 100 - 1 = 99 (ii) 99 - 3 = 96

(iii) 96 - 5 = 91 (iv) 91 - 7 = 84

(v) 84 - 9 = 75 (vi) 75 - 11 = 64

(vii) 64 - 13 = 51 (viii) 51 - 15 = 36

(ix) 36 - 17 = 19 (x) 19 - 19 = 0.

##### Question 92:

Find the square roots of the 729 by the prime factorisation Method.

##### Answer:

##### Question 93:

Find the square roots of the 400 by the prime factorisation Method.

##### Answer:

##### Question 94:

Find the square roots of the 1764 by the prime factorisation Method.

##### Answer:

##### Question 95:

Find the square roots of the 4096 by the prime factorisation Method.

##### Answer:

##### Question 96:

Find the square roots of the 7744 by the prime factorisation Method.

##### Answer:

##### Question 97:

Find the square roots of the 9604 by the prime factorisation Method.

##### Answer:

##### Question 98:

Find the square roots of the 5929 by the prime factorisation Method.

##### Answer:

##### Question 99:

Find the square roots of the 9216 by the prime factorisation Method.

##### Answer:

##### Question 100:

Find the square roots of the 529 by the prime factorisation Method.

##### Answer:

##### Question 101:

Find the square roots of the 8100 by the prime factorisation Method.

##### Answer:

##### Question 102:

Find the smallest whole number by which 252 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 103:

Find the smallest whole number by which 180 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 104:

Find the smallest whole number by which 1008 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 105:

Find the smallest whole number by which 2028 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 106:

Find the smallest whole number by which 1458 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 107:

Find the smallest whole number by which 768 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 108:

Find the smallest whole number by which 252 should be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 109:

Find the smallest whole number by which 2925 should be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 110:

Find the smallest whole number by which 396 should be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 111:

Find the smallest whole number by which 2645 should be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 112:

Find the smallest whole number by which 2800 should be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 113:

Find the smallest whole number by which 1620 should be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.

##### Answer:

##### Question 114:

The students of Class VIII of a school donated ₹2401 for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

##### Answer:

##### Question 115:

2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

##### Answer:

##### Question 116:

Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

##### Answer:

##### Question 117:

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

##### Answer:

##### Question 118:

##### Answer:

Yes.

##### Question 119:

Without calculating square roots, find the number of digits in the square root of the following numbers.

(i) 25600 (ii) 100000000 (iii) 36864

##### Answer:

We use bars to find the number of digits in the square root of a perfect square number.

##### Question 120:

Estimate the value of the following to the nearest whole number:

##### Answer:

##### Question 121:

Find the square root of 2304 by Division Method.

##### Answer:

##### Question 122:

Find the square root of 4489 by Division Method.

##### Answer:

##### Question 123:

Find the square root of 3481 by Division Method.

##### Answer:

##### Question 124:

Find the square root of 529 by Division Method.

##### Answer:

##### Question 125:

Find the square root of 3249 by Division Method.

##### Answer:

##### Question 126:

Find the square root of 1369 by Division Method.

##### Answer:

##### Question 127:

Find the square root of 5776 by Division Method.

##### Answer:

##### Question 128:

Find the square root of 7921 by Division Method.

##### Answer:

##### Question 129:

Find the square root of 576 by Division Method.

##### Answer:

##### Question 130:

Find the square root of 1024 by Division Method.

##### Answer:

##### Question 131:

Find the square root of 3136 by Division Method.

##### Answer:

##### Question 132:

Find the square root of 900 by Division Method.

##### Answer:

##### Question 133:

Find the number of digits in the square root of 64 (without any calculation).

##### Answer:

As we know that the square root of 2-digit
number is a single digit number, square root
of three or four digit number is a two-digit
number, square root of five or six digit number
is a 3 digit number and so on... .

64 is a two digit number. Therefore, the
number of digits in its square root is 1.

##### Question 134:

Find the number of digits in the square root of 144 (without any calculation).

##### Answer:

As we know that the square root of 2-digit
number is a single digit number, square root
of three or four digit number is a two-digit
number, square root of five or six digit number
is a 3 digit number and so on... .

144 is a three digit number. Therefore,
the number of digits in its square root
is 2.

##### Question 135:

Find the number of digits in the square root of 4489 (without any calculation).

##### Answer:

As we know that the square root of 2-digit
number is a single digit number, square root
of three or four digit number is a two-digit
number, square root of five or six digit number
is a 3 digit number and so on... .

4489 is a four digit number. Therefore,
the number of digits in its square root
is 2.

##### Question 136:

Find the number of digits in the square root of 27225 (without any calculation).

##### Answer:

As we know that the square root of 2-digit
number is a single digit number, square root
of three or four digit number is a two-digit
number, square root of five or six digit number
is a 3 digit number and so on... .

27225 is a five digit number. Therefore,
the number of digits in its square root
is 3.

##### Question 137:

Find the number of digits in the square root of 390625 (without any calculation).

##### Answer:

As we know that the square root of 2-digit
number is a single digit number, square root
of three or four digit number is a two-digit
number, square root of five or six digit number
is a 3 digit number and so on... .

390625 is a six digit number. Therefore,
the number of digits in its square root is 3.

##### Question 138:

Find the square root of 2.56.

##### Answer:

##### Question 139:

Find the square root of 7.29.

##### Answer:

##### Question 140:

Find the square root of 51.84.

##### Answer:

##### Question 141:

Find the square root of 42.25.

##### Answer:

##### Question 142:

Find the square root of 31.36.

##### Answer:

##### Question 143:

Find the least number which must be subtracted from 402 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

402

##### Question 144:

Find the least number which must be subtracted from 1989 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 145:

Find the least number which must be subtracted from 3250 so as to get a perfect square. Also, find the square root of the perfect square so obtained.##### Answer:

##### Question 146:

Find the least number which must be subtracted from 825 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 147:

Find the least number which must be subtracted from 4000 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 148:

Find the least number which must be added to 525 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

525

##### Question 149:

Find the least number which must be added to 1750 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 150:

Find the least number which must be added to 252 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 151:

Find the least number which must be added to 1825 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 152:

Find the least number which must be added to 6412 so as to get a perfect square. Also, find the square root of the perfect square so obtained.

##### Answer:

##### Question 153:

Find the length of the side of a square whose area is 441 m^{2}.

##### Answer:

##### Question 154:

In a right triangle ABC, $\angle $B = 90$\xb0$.

(a) If AB = 6 cm, BC = 8 cm, Find AC.

(b) If AC = 13 cm, BC = 5 cm, Find AB.

##### Answer:

##### Question 155:

A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

##### Answer:

Total no. of available plants = 1000

$\therefore $ Minimum number of more plants he needs = 124 – 100

= 24 plants

i.e., 1000 + 24 = 1024

$\therefore $ No. of plants in a rwo and a column

##### Question 156:

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.