# Class 8 ICSE Maths Solutions Chapter 4

## Class 8 ICSE Maths Solutions Chapter 4 Cubes and Cube Roots (Selina Concise)

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Selina Class 8 ICSE Math Book, Chapter 4, Cubes and Cube Roots. Here students can easily find step by step solutions of all the problems for Cubes and Cube Roots, Exercise 4A and 4B 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 4 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

Cubes and Cube Roots Exercise 4(A) Solution :

Question no – (1)

Solution :

(i) 7

= (7) ³ = 343

Thus, the cube of 7 is 343

(ii) 11

= (11)³ = 1331

Hence, the cube of 11 is 1331

(iii) 16

= (16)³ = 4096

So, the cube of 16 is 4096

(iv) 23

= (23)³ = 12167

Hence, the cube of 23 is 12167

(v) 31

= (31)³ = 29791

Thus, the cube of 31 is 29791

(vi) 42

= (42)³ = 74088

Therefore, the cube of 42 is 74088

Question no – (2)

Solution :

(i) 243

= 243 = 3 × 3 × 3 × 3 × 3

= (3 × 3 × 3) × 3 × 3

243 is not a perfect cube.

(ii) Given, 588

∴ 588 = 2 × 2 × 7 × 7 × 3

∴ It is not a perfect cube

(iii) 1331

1331 = 11 × 11 × 11

It is a perfect cube

(iv) 24000

24000 = (2 × 2 × 2) × (5 × 5 × 5) × (2 × 2 × 2) × 3

It is not perfect cube

(v) 1728

1728 = (2)³ × (2)³ × (3)³

It a perfect cube

(vi) 1938

1938 = 2 × 3 × 17 × 19

It is not a perfect cube.

Question no – (3)

Solution :

(i) 2.1

= (2.1)³

= (2.1 × 2.1 × 2.1)

= 9.261

So, the cube of 2.1 is 9.261

(ii) 0.4

= (0.4)³

= (0.4 × 0.4 × 0.4)

= 0.064

Thus, the cube of 0.4 is 0.064

(iii) 1.6

= (1.6)³

= (1.6 × 1.6 × 1.6)

= 4.096

Hence, the cube of 1.6 is 4.096

(iv) 2.5

= (2.5)³

= 15.625

So, the cube of 2.5 is 15.625

(v) 0.12

= (0.12)³

= 0.001728

Thus, the cube of 0.12 is 0.001728

(vi) 0.02

= (0.02)³

= 0.000008

Hence, the cube of 0.02 is 0.000008

(vii) 0.8

= (0.8)³

= 0.512

Therefore, the cube of 0.8 is 0.512

Question no – (4)

Solution :

(i) 3/7

= (3/7)³

= 27/343

Thus, the cube of 3/7 is 27/343.

(ii) 8/9

= (8/9)³

= 512/729

Hence, the cube of 8/9 is 512/729.

(iii) 10/13

= (10/13)³

= 1000/2197

Thus, the cube of 10/13 is 1000/2197.

(iv) 1 2/7

(1 2/7)³

= (9/7)³

= 729/543

So, the cube of 1 2/7 is 729/543.

(v) 2 1/2

= (2 1/2)³

= (5/2)³

= 125/8

Therefore, the cube of 2 1/2 is 125/8.

Question no – (5)

Solution :

(i) -3

= (-3)³

= (-3 × -3 ×-3)

= -27

Hence, the cube of -3 is -27

(ii) -7

= (-7)³

= (-7 × -7 × -7)

= -343

Thus, the cube of -7 is -343

(iii) -12

= (-12)³

= (-12 × -12 × -12)

= -1728

So, the cube of -12 is -1728

(iv) -18

= (-18)³

= -5832

Thus, the cube of -18 is -5832

(v) -25

= (-25)³

= -15625

Hence, the cube of -25 is -15625

(vi) -50

= (-50)³

= -125000

Therefore, the cube of -50 is -125000

Question no – (6)

Solution :

As per the given question,

216 = (6)³

729 = (9)³

3375 = (15)³

8000 = (20)³

125 = (5)³

343 = (7)³

4096 = (16)³

(i) Cube of an even number are – 216, 8000, 4096.

(ii) Cubes of an odd number are – 729, 3375, 125, 343, 9261.

Question no – (7)

Solution :

Given number, 1323

1323 = (3 × 3 × 3) × 7 ×7

Therefore, the least no is 7 must be multiplied.

Question no – (8)

Solution :

Given number, 8768

8768 = (2 × 2 × 2) × (2 × 2 × 2) × 137

Therefore, 8768 must be divided by 137.

Question no – (9)

Solution :

Given number, 27783

27783 = (3 × 3 × 3) × 3 × (7 ×7 × 7)

Therefore, 27783 must be multiplied by 3 × 3 = 9

Question no – (10)

Solution :

Given in the question, 8640

8640 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × 5

Therefore,  8640 must be divided by 5.

Question no – (11)

Solution :

Given number, 77175

77175 = (7 × 7 × 7) × 3 × 5 × 5

Therefore, 77175 must be multiplied by 15

Cubes and Cube Roots Exercise 4(B) Solution :

Question no – (1)

Solution :

(i) 64

= ∛64

= 4

Thus, the cube-root of 64 is 4.

(ii) 343

= ∛343

= 7

Hence, the cube-root of 343 is 7.

(iii) 729

= ∛729

= 9

So, the cube-root of 729 is 9.

(iv) 1728

= ∛1728

= 12

Thus, the cube-root of 1728 is 12.

(v) 9261

= ∛9261

= 21

So, the cube-root of 9261 is 21.

(vi) 4096

=∛4096

= 16

Thus, the cube-root of 4096 is 16.

(vii) 8000

= ∛8000

= 20

Hence, the cube-root of 8000 is 20.

(viii) 3375

= ∛3375

= 15

Therefore, the cube-root of 3375 is 15.

Question no – (2)

Solution :

(i) 27/64

∛27/64

=√3 × 3 × 3/4 × 4 × 4

= 3/4

The cube root of 27/64 is 3/4

(ii) 125/216

∛125/216

= √5 × 5 × 5/6 × 6 × 6

= 5/6

The cube root of 125/216 is 5/6

(iii) 343/512

∛343/512

= √7 × 7 × 7/8 × 8 × 8

= 7/8

The cube root of 343/512 is 7/8

(iv) 64 × 729

∛64 × 729

= 4 × 9

= 36

The cube root of 64 × 729 is 36

(v) 64 × 27

∛64 × 27

= √4 × 4 × 4 × 3 × 3 × 3

= 4 × 3

= 12

The cube root of 64 × 27 is 12

(vi) 729 × 8000

∛729 × 8000

= √9 × 9 × 9 × 20 × 20 × 20

= 9 × 20

= 180

The cube root of 729 × 8000 is 180

(vii) 3375 × 512

∛3375 × 512

= √15 × 15 × 15 × 8 × 8 × 8

= 15 × 8

= 120

The cube root of 3375 × 512 is 120

Question no – (3)

Solution :

(i) -216

∛- 216

= √ -6 × -6 × -6

= -6

So, the cube root of -216 is -6.

(ii) -512

∛- 512

= √- 8 × -8 × -8

= -8

Hence, the cube root of -512 is -8.

(iii) -1331

∴ ∛-1331

= √- 11 × -11 × -11

= -11

Therefore, the cube root of -1331 is -11

(iv) -27/125

∛- 27/125

= √- 3 × -3 × -3/- 5 × -5 × -5

= -3/5

Thus, the cube root of -27/125 is -3/5.

(v) -64/343

∛- 64/343

= √- 4 × -4 × -4/7 × 7 × 7

= -4/7

Hence, the cube root of -64/343 is -4/7

(vi) -2197

∛- 2197

= √-13 × -13 × -13

= -13

So, the cube root of -2197 is -13

(vii) -512/343

∛- 512/343

= √ -8 × -8 × -8/7 × 7 × 7

= -8/7

So, the cube root of -512/343 is -8/7.

(viii) -5832

∛-5832

= √ -2 × -2 × -2 × -3 × -3 × -3 × -3 × -3 × -3

= -2 × -3 × -3

= -18

Therefore, the cube root of -5832 is -18.

Question no – (4)

Solution :

(i) 2.744

= 3√2.744

= 3√2744/1000

= 14/10

= 1.4

So, the cube root of 2.744 is 1.4

(ii) 9.261

= 3√9.261

= 3√9261/1000

= 21/10

Hence, the cube root of 9.261 is 21/10

(iii) 0.000027

= 3√27/1000000

= 3√3 × 3 × 3/100 × 100 × 100

= 3/100

= 0.03

So, the cube root of 0.000027 is 0.03.

(iv) -0.512

= 3√-0.512

= 3√-512/1000

= √-8 × -8 × -8/10 × 10 × 10

= -8/10

= -0.8

Therefore, the cube root of -0.512 is -0.8

(v) -15.625

= 3√-15625/1000

= 3√-25 × -25 × -25/10 × 10 × 10

= -25/10

= -2.5

Thus, the cube root of -15.625 is -2.5

(vi) -125 × 1000

= 3√-5 × -5 × -5 × 10 × 10 × 10

= -5 × 10

= -50

The cube root of -125 × 1000 is -50.

Question no – (5)

Solution :

In the given question, 26244

3√26244

= 2 × 2 × (3 × 3 × 3) × (3 × 3 × 3) × 3 × 3

Therefore, 26244 must be divided by 36.

Question no – (6)

Solution :

In the given question, 30375

30375 = (3 × 3 × 3) × (5 × 5 × 5) × 3 × 3

Therefore, 30375 must be multiplied by 3

Question no – (7)

Solution :

(i) Given, 700 × 2 × 49 × 5

= 3√700 × 2 × 49 × 5

= 3√2 × 2 × 2 × 5 × 5 × 7 × 7 × 7 × 5

= 2 × 5 × 7

= 70

Therefore, the cube-roots of 700 × 2 × 49 × 5 is 70.

(ii) -216 × 1728

∛- 216 × 1728

= -3√-6 × -6 × 12 × 12 × 12

= -6 × 12

= -72

Thus, the cube root of -216 × 1728 is -72.

(iii) -64 × -125

= 3√ -4 × -4 × -4 × -5 × -5 × -5

= (-4 × -5)

= 20

Hence, the cube root of -64 × -125 is 20 .

(iv) -27/343

= 3√- 3 × -3 × -3/7 × 7 × 7

= -3/7

So, the cube root of -27/343 is -3/7

(v) 729/-1331

∛9 × 9 × 9/-11 × -11 × -11

= -9/11

Therefore, the cube root of 729/-1331 is -9/11.

(vi) 250.047

= 250047/1000

= (3 × 3 × 3) × (3 × 3 × 3) × (7 × 7 × 7)

= 3 × 3 × 7

= 63

63/10

= 6.3

Therefore, the cube root of 250.047 is 6.3

Next Chapter Solution :

Updated: June 20, 2023 — 2:01 pm