# Maths Wiz Solutions Class 8 Chapter 3

## Maths Wiz Class 8 Solutions Chapter 3 Squares and Square Roots Cubes and Cube Roots

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Wiz Class 8 Math Book, Chapter 3, Squares and Square Roots Cubes and Cube Roots. Here students can easily find step by step solutions of all the problems for Squares and Square Roots Cubes and Cube Roots, Exercise 3A, 3B, 3C, 3D and 3E Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 3 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

Squares and Square Roots Cubes and Cube Roots Exercise 3A Solution :

Question no – (1)

Solution :

(a) 122

= 12 × 12

= 144

(b) 92

= 9 × 9

= 81

(c) 282

= 28 × 28

= 784

(d) 392

= 39 × 39

= 1521

(e) 2152

= 215 × 215

= 46225

Question no – (2)

Solution :

(a) 784 = Perfect Square

(b) 1296 = Perfect Square

(c) 7500 = Not perfect square

(d) 5184 = Perfect square

(e) 980 = Not perfect square

(f) 4050 = not perfect square

Question no – (3)

Solution :

(a) 240 ∴ 240 = 4 × 4 × 3 × 5

The smallest number is – 15

(b) 432 432 = 4 × 4 × 17

The smallest number is 17

(c) 2592 2592 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

The smallest number is = 2

(d) 18000 18000 = 4 × 4 × 3 × 3 × 5 × 5 × 5

The smallest number is = 5

(e) 21952 21952 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7

The smallest number is = 17

Question no – (4)

Solution :

(a) 98 98 = 2 × 7 × 7

The divider is 2

(b) 363 363 = 3 × 11 × 11

The divider is 3

(c) 700 700 = 2 × 2 × 5 × 5 × 7

The divider is 7

(d) 4400 44000 = 2 × 2 × 2 × 2 × 5 × 5 × 11

The divider is 11

(e) 4374 4374 = 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3

The divider is = 2 × 3

= 6

Question no – (5)

Solution :

(a) 537

(b) 1042

(c) 6398

(g) 33493

These are not perfect squares because a square number cannot have 2, 3, 7 or 8 at the unit place.

(h) 960

(i) 72000

These are not perfect squares because, a whole numbers having odd number of zeros at the end cannot be a perfect square.

(c) 800

(d) 384

(e) 625

(j) 1571

May be perfect squares.

Question no – (6)

Solution :

(a) 6092

The unit digit squares = 92 = 81

(b) 3272

The unit squares = 72 = 49

(c) 3252

The unit digit square = 52 = 25

(d) 3412

The unit digit squares = 12 = 1

(e) 5462

The unit square digit square = 62 = 36

Therefore, (a) 6092 (d) 3412 would end with the digit 1.

Question no – (7)

Solution :

As per the given numbers only,

(c) 2762 have digit 6 at unit places.

Question no – (8)

Solution :

(a) 642

= The unit digit square = 42 = 16

The unit digit of the squares is 6

(b) 932

= The unit digit squares = 32 = 9

The unit digit of the square is 9

(c) 2062

The unit digit square = 62 = 36

The unit digit of the squares is 6

(d) 1352

= The unit digit squares = 52 = 25

The unit digit of the square is 5

(e) 4992

= The unit digit square = 92 = 81

The unit digit of the square = 1

(f) 2382

= The unit digit square = 82 = 64

The unit digit of the square 4

(g) 6072

= The unit digit square = 72 = 49

The unit digit of the square 9

(h) 6522

The unit square = 22 = 4

The unit digit of two square is = 4

(i) 6502

The unit digit square = 02 = 00

The unit digit of the square is = 0

(j) 9712

The unit digit square =m 12 = 1

The unit digit of the square is 1

Question no – (9)

Solution :

The square of odd numbers are odd numbers and the square of even numbers are even numbers.

Therefore,

(a) 517 (e) 945 (f) 719 are Odd.

(b) 234 (c) 300 (d) 718 are Even.

Question no – (10)

Solution :

(a) 40

(0)2 = 00

The number of zero is 2

(b) 400

(00)2 = 0000

The number of zero is 4

(c) 8000

= (000)2 = 000000

The number of zero is 6

(d) 60,000

= (0000)2 = 00000000

The number of zero is 8

Question no – (11)

Solution :

(a) 62 and 72

= Number of numbers lying between 62 and 72 are,

= 2 × 6 = 12

(b) 192 and 202

= Number of numbers lying between 192 and 202 are,

= 2 × 19 = 38

(c) 492 and 502

= Number of numbers lying between 492 and 502 are,

= 2 × 49 = 98

(d) 752 and 762

= Number of numbers lying between 752 and 762 are,

= 2 × 75 = 150

Question no – (12)

Solution :

(a) 1002 and 1012

Non –square numbers lie between 1002 and 101are,

= 2 × 100 = 200

(b) 2152 and 2162

Non-square numbers lie between 2152 and 2162 are,

= 2 × 215 = 430

(c) 5002 and 5012

Non-square numbers lie between 5002 and 5012 are,

= 2 × 500 = 1000

Question no – (13)

Solution :

(a) 232

= 232-1/2 + 232 + ½

= 529 –1/2 + 529 +1/2

= 528/2 + 530/2

= 264 + 265

= 529

(b) 152

= 152 – 1/2 + 152 + ½

= 224/2 + 226/2

= 112 + 113

= 225

(c) 192

= 192-1/2 + 192+1/2

= 360/2 + 362/2

= 180 + 181

= 361

(d) 252

= 252-1/2 + 252+1/2

= 624/2 + 626/2

= 312 + 313

= 625

(e) 172

= 172-1/2 + 172+1/2

= 288/2 + 280/2

= 144 + 145

= 289

Question no – (14)

Solution :

(a) 242 – 232

= 24 + 23

= 47

(b) 592 – 582

= 59 + 58

= 117

(c) 752 – 742

= 75 + 74

= 149

(d) 1022 – 1012

= 102 + 101

= 203

Question no – (15)

Solution :

(a) 1 + 3 + 5 + 7 + 9

= sum of first 5 odd numbers

= 52 = 25

(b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

= sum of first 10 odd numbers

= 102 = 100

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

Given series,

= sum of first 12 odd numbers

= 122 = 144

Question no – (16)

Solution :

(a) Given number, 169

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25

(b) Given number, 64

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

Question no – (18)

Solution :

112 = 121

1012 = 10201

10012 = 1002001

100012 = 100020001

1000012 = 10000200001

100000012 = 100000020000001

Question no – (19)

Solution :

12 + 22 + 22 = 32

22 + 32 + 62 = 72

32 + 42 + 122 = 132

42 + 52 + 52 = 212

52 + 62 + 302 = 312

62 + 72 422 = 432

Therefore, the missing numbers are 5, 6, and 7, 42

Squares and Square Roots Cubes and Cube Roots Exercise 3B Solution :

Question no – (1)

Solution :

(a) 4 = 2 × 2

and also 4 = (-2) × (-2)

2 and (-2) are roots of 4

(b) 81 = 9 × 9

also 81 = (-9) × (-9)

9 and (-9) are roots of 81

(c) 196 = 14 × 14

also 196 = (-14) × (-14)

(-14) and 14 are roots of 196

(d) 400 = 20 × 20

also 400 = (-20) × (-20)

20 and (-20) are roots of 400

(e) 441 = 21 × 21

also 441 = (-21) × (-21)

20, (-21) are roots of 441

(f) 0.0049 = 0.07 × 0.07 also

0.0049 = (-0.07) × (-0.07)

0.07 and (-0.07) are roots of 0.0049

(g) 0.0001 = 0.01 × 0.01

also 0.0001 = (-0.01) × (-0.01)

(0.01) and (-0.01) are roots of 0.0001

(h) 3 1/16 = 49/16 = 7/4 × 7/4 also

49/16 = (- 7/4) × (- 7/4)

(- 7/4) and 7/4 are roots of 3 1/16

(i) 2/14 = 9/4 = 3/2 × 3/2 also

9/4 = (- 3/2) × (- 3/2)

(- 3/2) and 3/2 are roots of 2 1/4

(j) 0.0289 = 0.17 × 0.17 also

0.0289 = (-0.17) × (-0.17)

(-0.17) and (0.17) are roots of 0.0289

Question no – (2)

Solution :

(a) √36

= √6 × √6

= 6

(b) – √9

= √3 × 3

= -3

(c) √121

= √11 × 11

= 11

(d) – √225

= -√15 × 15

= -15

(e) √361

= √19 × 19

= 19

(f) √900

= √30 × 30

= 30

(g) √0.09

= √0.3 × 0.3

= 0.3

(h) √0.0256

= √0.16 × 0.16

= 0.16

(i) √2.25

= √1.5 × 1.5

= 1.5

(j) √4 25/36

= √169/36

= √13 × 13/6 × 6

= 13/6

Question no – (3)

Solution :

(a) x2 = 1

or, x = ± 1   ….(Solved)

(b) 12 x2 = 108

or, x2 = 108/12

or, x= 9

or, x = √9

=  ± 3   ….(Solved)

(c) x2 – 17 = – 1

or, x= 17 – 1

or, x = √16

= ± 4   ….(Solved)

(d) x= 16/25

or, x = ± 4/5   ….(Solved)

Question no – (4)

Solution :

(a) 484

= 484 = 2 × 2 × 11 × 11

√484 = 2 × 11

= 22

(b) 2500

= 2500 = 5 × 5 × 10 × 10

√2500

= 5 × 10

= 50

(c) 2025

= 2025 = 5 × 5 × 3 × 3 × 3 × 3

√2025

= 5 × 3 × 3

= 45

(d) 2916

= 2916 = 2 × 2 × 3 × 3 × 9 × 9

√2916

= 2 × 3 × 9

= 54

(e) 2401

= 2401 = 7 × 7 × 7 × 7

√2401

= √7 × 7 × 7 × 7

= 7 × 7

= 49

(f) 6084

= 6084 = 2 × 2 × 3 × 3 × 13 × 13

√6084

= 2 × 3 × 13

= 78

(g) 1 184/441

= 1 184/441 = 625/441

= 5 × 5 × 5 × 5 / 3 × 7 × 3 × 7

√1 184/441

= 5 × 5/3 × 7

= 25/21

(h) 0.1936

= 0.1936 = 1936/10000

= 4 × 4 × 11 × 11/100 × 100

√0.1936

= 4 × 11/100

= 44/100

= 0.44

(i) 0.0576

= 0.0576 = 576/10000

= 2 × 2 × 12 × 12/100 × 100

√0.0576

= 2 × 12/ 100

= 0.24

(j) 40.96

=  40.96 = 4096/100

= 4 × 4 × 4 × 4 × 4 × 4/10 × 10

√40.96

= 4 × 4 × 4 / 10

= 6.4

Question no – (5)

Solution :

(a) 768 = 768 = 4 × 4 × 4 × 4 × 3

To make 768 a perfect square it should be multiplied by 3

(b) 200 = 200 = 2 × 2 × 5 × 5 × 2

To make 200 perfect square it should be multiplied by 2

(c) 2880 = 2880 = 4 × 4 × 2 × 2 × 3 × 3 × 5

To make 2880 perfect square it should be multiplied by 5

(d) 16807 = 16807 = 7 × 7 × 7 × 7 × 7

To make 16807 perfect square it should be multiplied by 7

(e) 1331 = 1331 = 11 × 11 × 11

To make 1331 perfect square it should be multiplied by 11

Question no – (6)

Solution :

(a) 3125 3125 = 5 × 5 × 5 × 5 × 5

The divider will be 5

(b) 1800 1800 = 3 × 3 × 10 × 10 × 2

The divider will be 2

(c) 1008 1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7

The divider will be 7

(d) 6912 6912 = 3 × 3 × 4 × 4 × 4 × 4 × 3

The divider will be 3

(e) 2925 2925 = 5 × 5 × 3 × 3 × 13

The divider will be 13

Question no – (7)

Solution : LCM of 8, 15 and 20 = 120

120 = 2 × 2 × 2 × 5 × 3

The factor 30 remains unpaired

Hence, the smallest square number divisible by 8, 15, 20 is 120 × 30 = 3600

The required number is 3600.

Question no – (8)

Solution : LCM of 3, 4, 5, 6, 8

120 = 2 × 2 × 3 × 5 × 2

The factor 30 remains unpaired

Hence the least square number divisible by 3, 4, 5, 6, 8 is 120 × 30 = 3600

Therefore, the least number will be 3600

Question no – (9)

Solution :

Let the length of side of the plat = a

a2 = 101 1/400

a2 = 40401/400

a = √201 × 201/20 × 20

a = Length of side = 10 1/20 m.

Therefore, the length of one side of the plot will be 10 1/20 m.

Question no – (10)

Solution :

√162 + √138 + √121

= √162 + √38 + √11 × 11

= √162 + √38 + 11

= √162 + √49

= √162 + 7

= √169

= √13 × 13

= 13

Therefore, the value will be 13.

Question no – (11)

Solution :

√3136 = 56

= √31.36 + √0.3136

= √3136/100 + √3136/10000

= √56 × 56/10 × 10 + √56 × 56/100 × 100

= 56/10 + 56/100

= 5.6 + 0.56

= 6.16

Therefore, the value will be 6.16

Squares and Square Roots Cubes and Cube Roots Exercise 3C Solution :

Question no – (1)

Solution :

(a) 484 √484 = 22

(b) 841 √841 = 29

(c) 1849 √1849 = 43

(d) 2704 √2704 = 52

(e) 4624 √4624 = 68

(f) 6724 √6724 = 82

(g) 7569 √7569 = 87

(h) 9801 √9801 = 99

Question no – (2)

Solution :

(a) 7 522/529

= 4225/529

= √4225/529 = 65/23

(b) 8 617/784

= 6889/784

= √6889/784 = 83/28

(c) 2 766/2209

= 5184/2209

= √5184/2209 = 72/47

Question no (3)

Solution :

(a) 3.24 √3.24 = 1.8

(b) 6.25 √6.25 = 2.5

(c) 11.56 √11.56 = 3.4

(d) 16.81 √16.81 = 4.1

(e) 22.09 √22.09 = 4.7

(f) 0.5041 √0.5041 = 0.71

(g) 0.5625 √0.5625 = 0.75

(h) 0.9216 √0.9216 = 0.96

Squares and Square Roots Cubes and Cube Roots Exercise 3D Solution :

Question no – (1)

Solution :

(a) 740 The subtracted number 11

(b) 1535 The subtracted number 9

(c) 7926 The subtracted number 5

Question no – (2)

Solution :

(a) 708 We observe that 262 <708 <272

272 – 708

= 729 – 708 = 21

Then, 708 would become

708 + 21 = 729 and

√729 = 27

(b) 1840 We observe that

42 < 1840 <432

= 432 – 1840

= 1849 – 1840

= 9

(c) 3219 We observe that

562 < 3219 < 572

= 572 – 3219

= 3249 – 3219

= 30

Question no – (3)

Solution :

Total number of soldiers – 4225 since there are as many rows as the number of soldiers in a row.

√3364 = 65

The number of rows = 65 Question no – (4)

Solution :

Total number of plants = 3364

Since there are as many rows as there are trees in a row.

√3364 = 58

The number of rows = 58 Question no – (5)

Solution :

Total number of charity- 7225

Since each member contributed as many rupees as there were number of members.

√7225 = 85

The number of members in the club = 85 Squares and Square Roots Cubes and Cube Roots Exercise 3E Solution :

Question no – (1)

Solution :

(a) 12

= (12)3 = 12 × 12 × 12

= 1728

So, the cube of 12 is 1728

(b) 15

= (15)3 = 15 × 15 × 15

= 3375

Thus, the cube of 15 is 3375

(c) 30

= (30)3 = 30 × 30 × 30

= 27000

Thus, the cube of 30 is 27000

(d) 200

= (200)3 = 200 ×200 × 200

= 8000000

Thus, the cube of 200 is 8000000

(e) -3/7

= (-3/7)3 = (-3/7) × (- 3/7) × (- 3/4)

= – 27/343

Thus, the cube of -3/7 is – 27/343

(f) 1 3/8

= 1 3/8 = (11/8)3

= 11 × 11 × 11/8 × 8 × 8

= 1331/512

Thus, the cube of 1 3/8 is 1331/512

(g) 0.4

= (0.4)3 = (4/10)3

= 64/1000

= 0.064

Thus, the cube of 0.4 is 0.064

(h) 0.9

= (0.9)3 = (9/10)3

= 7291/1000

= 0.729

Thus, the cube of 0.9 is 0.729

(i) 0.02

= (0.02)3 = (2/100)3

= 8/1000000

= 0.000008

Thus, the cube of 0.02 is 0.000008

(j) -2 2/9

= -2 2/9 = (-20/9)3

= (- 20/9) × (-20/9) × (-20/9)

= – 8000/729

Thus, the cube of -2 2/9 is – 8000/729

Question no – (2)

Solution :

(a) 125 125 = 5 × 5 × 5

3 √125 = 5

It is a perfect cube.

(b) 2197 2197 = 13 × 13 × 13

3√2197 = 13

It is a perfect cube.

(c) 832 832 = 2 × 2 × 2 × 2 × 2 × 2 × 13

832 is not a perfect cube.

(d) 2744 2744 = 14 × 14 × 14

3√2744 = 14 is a perfect cube

(e) 2000 2000 = 10 × 10 × 10 × 2

2000 is not a perfect cube.

Question no – (3)

Solution :

(a) 36

36 = 6 × 6

The multiplier is 6 so

36 = 6 × 6 × 6

∴ 3 √36 = 6

(b) 121

121 = 11 × 11

The multiplier is 11 so

121 = 11 × 11 × 11

3 √121 = 11

(c) 392

392 = 2 × 2 × 2 × 7 × 7

The multiplier is 7 so

392 = 2 × 2 × 2 × 7 × 7 × 7

3 √392 = 2 × 7 = 14

Question no – (4)

Solution :

(a) 54 54 = 3 × 3 × 3 × 2

The divider is 2

27 = 3 × 3 × 3

(b) 625 625 = 5 × 5 × 5 × 5

The divider is 5

125 = 5 × 5 × 5

(c) 1536 1536 = 3 × 3 × 3 × 3 × 19

The divider is = 3 × 19

(d) 7000 7000 = 10 × 10 × 10 × 7

The divider is 7

Question no – (5)

Solution :

(a) 8

= 2 × 2 × 2

3√8 = 2

The cube root of 8 is 2

(b) 216

= 2 × 2 × 2 × 3 × 3 × 3

3√216 = 2 × 3 = 6

The cube root of 216 is 6

(c) 1728

= 4 × 4 × 4 × 3 × 3 × 3

3√1728 = 4 × 3 = 12

The cube root of 1728 is 12

(d) – 4 17/27

= – (125/27)

= – (5 × 5 × 5/3 × 3 × 3)

– 3√125/27 = – 5/3

The cube root of -4 17/27 is -5/3

(e) 0.027

= 27/1000

= 3 × 3 × 3/10 × 10 × 10

3√0.027 = 3/10 = 0.3

The cube root of 0.027 is 0.3

(f) – 0.216

= – 216/1000

= – 6 × 6 × 6/10 × 10 × 10

– 3√0.216 = – 6/10 = 0.6

The cube root of -0.216 is 0.6

(g) 0.001331

= 1331/1000000

= 11 × 11 × 11/100 × 100 × 100

3√0.001331 = 11/100 = 0.11

The cube root of 0.001331 is 0.11

(h) 0.002744

= 2744/1000000

= 2 × 2 × 2 × 7 × 7 × 7/100 × 100 × 100

∴ 3√0.002744 = 2 × 7/100

= 14/100

= 0.14

The cube root of 0.002744 is 0.14

Next Chapter Solution :

Updated: June 19, 2023 — 7:37 am