## Selina Concise Mathematics Class 8 ICSE Solutions Chapter 4 Cubes and Cube-Roots (Including use of tables for natural numbers)

**Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 4 Cubes and Cube-Roots (Including use of tables for natural numbers)**

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### Cubes and Cube-Roots Exercise 4A – Selina Concise Mathematics Class 8 ICSE Solutions

**Question 1.**

Find the cube of :

(i) 7

(ii) 11

(iii) 16

(iv) 23

(v) 31

(vi) 42

(vii) 54

**Solution:**

(i) (7)^{3} = 7 x 7 x 7 = 343

(ii) (11)^{3} =11 x 11 x 11 = 1331

(iii) (16)^{3} = 16 x 16 x 16 = 4096

(iv) (23)^{3} = 23 x 23 x 23 = 12167

(v) (31)^{3} = 31 x 31 x 31 = 29791

(vi) (42)^{3} = 42 x 42 x 42 = 74088

(vii) (54)^{3} = 54 x 54 x 54 = 157464

**Question 2.**

Find which of the following are perfect cubes :

(i) 243

(ii) 588

(iii) 1331

(iv) 24000

(v) 1728

(vi) 1938

**Solution:**

1938 = 2 x 3 x 17 x 19

1938 is not a perfect cube.

**Question 3.**

Find the cubes of :

(i) 2.1

(ii) 0.4

(iii) 1.6

(iv) 2.5

(v) 0.12

(vi) 0.02

(vii) 0.8

**Solution:**

**Question 4.**

Find the cubes of :

(i) \(\frac { 3 }{ 7 }\)

(ii) \(\frac { 8 }{ 9 }\)

(iii) \(\frac { 10 }{ 13 }\)

(iv) \(1\frac { 2 }{ 7 }\)

(v) \(2\frac { 1 }{ 2 }\)

**Solution:**

**Question 5.**

Find the cubes of :

(i) -3

(ii) -7

(iii) -12

(iv) -18

(v) -25

(vi) -30

(vii) -50

**Solution:**

**Question 6.**

Which of the following are cubes of:

(i) an even number

(ii) an odd number

216, 729, 3375, 8000, 125, 343, 4096 and 9261.

**Solution:**

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

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

**Question 7.**

Find the least number by which 1323 must be multiplied so that the product is a perfect cube.

**Solution:**

The prime factor of 1323 are =3 x 3 x 3 x 7 x 7

= (3 x 3 x 3) x 7 x 7

Clearly, 1323 must be multiplied by 7.

**Question 8.**

Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.

**Solution:**

**Question 9.**

Find the smallest number by which 27783 be multiplied to get a perfect square number.

**Solution:**

**Question 10.**

With what least number must 8640 be divided so that the quotient is a perfect cube?

**Solution:**

**Question 11.**

Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?

**Solution:**

### Cubes and Cube-Roots Exercise 4B – Selina Concise Mathematics Class 8 ICSE Solutions

**Question 1.**

Find the cube-roots of :

(i) 64

(ii) 343

(iii) 729

(iv) 1728

(v) 9261

(vi) 4096

(vii) 8000

(viii) 3375

**Solution:**

**Question 2.**

Find the cube-roots of :

(i) \(\frac { 27 }{ 64 }\)

(ii) \(\frac { 125 }{ 216 }\)

(iii) \(\frac { 343 }{ 512 }\)

(iv) 64 x 729

(v) 64 x 27

(vi) 729 x 8000

(vii) 3375 x 512

**Solution:**

**Question 3.**

Find the cube-roots of :

(i) -216

(ii) -512

(iii) -1331

(iv) \(\frac { -27 }{ 125 }\)

(v) \(\frac { -64 }{ 343 }\)

(vi) \(\frac { -512 }{ 343 }\)

(vii) -2197

(viii) -5832

(ix) -2744000

**Solution:**

**Question 4.**

Find the cube-roots of :

(i) 2.744

(ii) 9.261

(iii) 0.000027

(iv) -0.512

(v) -15.625

(vi) -125 x 1000

**Solution:**

**Question 5.**

Find the smallest number by which 26244 may be divided so that the quotient is a perfect cube.

**Solution:**

The prime factors of 26244 are

Clearly, 26244 must be divided by

3 x 3 x 2 x 2 = 36

**Question 6.**

What is the least number by which 30375 should be multiplied to get a perfect cube?

**Solution:**

The prime factors of 30375 are

**Question 7.**

Find the cube-roots of :

(i) 700 x 2 x 49 x 5

(ii) -216 x 1728

(iii) -64 x -125

(iv) \(\frac { -27 }{ 343 }\)

(v) \(\frac { 729 }{ -1331 }\)

(vi) 250.047

(vii) -175616

**Solution:**