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**Frank Learning Maths Class 8 Solutions Chapter 4 Cubes and Cube Roots**

Welcome to NCTB Solution. Here with this post we are going to help 8th class students for the Solutions of Frank Learning Maths Class 8 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. Here students will find solutions for Exercise 4.1 and 4.2. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.

**Cubes and Cube Roots Exercise 4.1 Solution**

**Question no – (1) **

**Solution :**

**(a)** 23

**∴** (23)^{3}

= 23 × 23 × 23

= 12167

So, the cube of 23 is 12167

**(b)** 35

**∴** (35)^{3}

= 35 × 35 × 35

= 42,875

Hence, the cube of 35 is 42875

**(c)** 17

**∴** (17)^{3}

= 17 × 17 × 17

= 4913

Thus, the cube of 17 is 4913

**(d)** 42

**∴** (42)^{3}

= 42 × 42 × 42

= 74088

Therefore, the cube of 42 is 74088

**Question no – (2) **

**Solution : **

**(a)** Given number, -15

**∴** (-15)^{3}

= -(15 × 15 × 15)

= -3375

Hence, the cube of -15 is -3375

**(b)** Given number, -21

**∴** (-21)^{3}

= -(21 × 21 × 21)

= -9261

Therefore, the cube of -21 is -9261

**(c)** Given number, 0.05

**∴** (0.05)^{3}

= (0.05 × 0.05 ×0.05)

= 0.000125

Thus, the cube of 0.05 is 0.000125

**(d)** Given number, 3.2

**∴** (3.2)^{3}

= 3.2 × 3.2 × 3.2

= 32.768

Therefore, the cube of 3.2 is 32.768

**(3) Find the cube of the following rational numbers**

**Solution : **

**(a)** -13/18

**∴** (-13/18)^{3}

= – (13^{3}/18^{3})

= 2196/5832

Hence, the cube of -13/18 is 2196/5832

**(b)** 27/32

**∴** (27/32)^{3}

= 27^{3}/32^{3}

= 19683/32768

Thus, the cube of 27/32 is 19683/32768

**(c)** 2 3/11

**∴** (25/11)^{3}

= 25^{3}/11^{3}

= 15625/1331

So, the cube of 2 3/11 is 15625/1331

**(d)** -1 5/8

**∴** -13^{3}/8^{3}

= – 2197/512

Thus, the cube of -1 5/8 is -2197/512

**Question no – (4) **

**Solution : **

**(a)** Given number, 4608

4608 = 4 × 4 × 4 × 2 × 2 × 2 × 3 × 3

**∴ **Multiplied number 3

**(b)** Given number, 10584

**∴** 10584 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7

**∴** Multiplied number 7

**(c)** Given number, 26244

**∴** 26244 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3

**∴** The multiplied number 6

**Question no – (5) **

**Solution : **

**(a)** Given number, 4374

**∴** 4374 = 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3

**∴** Divided number 6

**(b)** Given number, 9408

**∴** 9408 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 3

**∴** Divided number 147

**(c)** Given number, 8575

**∴** 8575 = 5 × 5 × 7 × 7 × 7

**∴** Divided number 25

**(d)** Given number, 20736

**∴** 20736 = 2 × 2 × 2 × 2 × 2 × 2 × 4 × 9 × 9

**∴** Divided number should be 324

**Question no – (6) **

**Solution : **

**(a)** 7^{3} = 43 + 45 + 47 + 49 + 51 + 53 + 55

**(b)** 8^{3 }= 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71

**(c)** 10^{3 }= 91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107

**Question no – (8) **

**Solution : **

**(a)** Cube of any odd number is even → **False**

**(b)** A perfect cube does not end with two zeros → **True**

**(c)** If square of a number ends with 5, then its cube ends with 25 → **False**

**(d)** There is no perfect cube which ends with 8 → **False**

**(e)** The cube of a two digit number may be a three digit number → **False**

**(f)** The cube of a two digit number may have seven or more digits → **False**

**(g)** The cube of a single digit number may be a single digit number → **True**

**(h)** If x2 ends in 9, then x3 ends in 7 → **False**

**(i)** For an integer m, m3 is always greater than m2 → **False**

**(j)** If a is a factor of b, then a3 is a factor of b3 → **True**

**(k)** There is no perfect cube that ends in 7 → **False. **

**Cubes and Cube Roots Exercise 4.2 Solution**

**Question no – (1) **

**Solution : **

**(a)** Given, ∛0.13 × 0.13 × 0.13 × 65 × 65 × 65

= 0.13/100 × 65

= 8.75

**(b)** Given, ∛ -64 + ∛ 0.027/1000

= – 8 + 3/10

= -8 + 3

= – 8.3

**Question no – (2)**

**Solution : **

**(a) 6859**

The unit digit 9

Tens digit 1

**∴** The cube root of 6859 = 19

**(b) 24,389**

The unit digit = 9

tens digit = 2

**∴** The cube root = 29

**(c) 9261**

Unit digit = 1

Tens digit = 2

**∴** The cube root = 21

**(d) 15625**

Unit digit = 5

Tens digit = 2

**∴ **The cube root = 25

**Question no – (3) **

**Solution : **

**(a) -2197**

∴ 3√-2197

= -3√13 × 13 × 13

= -13

**(b) -5832**

∴ – 3√5832

= – 3√2 × 2 × 2 × 9 × 9 × 9

= – (2 × 9)

= – 18

**(c) 21952**

**∴** 3√21952

= 3√4 × 4 × 4 × 7 × 7 × 7

= 4 × 7

= 28

**(d) 13824**

**∴** 3√13824

= 3√4 × 4 × 4 × 6 × 6 × 6

= 4 × 6

= 24

**Question no – (4) **

**Solution : **

**(a) 729/1728**

= ∛729/1728

= ∛9 × 9 × 9 /12 × 12 × 12

= 9/12

**(b) -343/2197**

= ∛-343/2197

= ∛(-7) × (-7) /13 × 13 × 13

= -7/13

**(c) 0.004096**

∛0.004096/1000000

= ∛16 × 16 × 16 /100 × 100 × 100

= 16/100

= .16

**(d) -9.261**

= ∛- 9261/100

= ∛-21 × (-21) × (-21)/10 × 10 × 10

= -21/10

= – 2.1

**Question no – (5) **

**Solution : **

**(a)** 216 × 343

**∴** ∛216 × 343

= ∛6 × 6 × 6 × 7 × 7 × 7

= 6 × 7

= 42

Therefore, the cube root of 216 × 343 is 42

**(b)** 144 × 96

**∴** ∛144 × 96

= ∛12 × 12 × 4 × 2 × 12

= 12 × 12

= 24

Hence, the cube root of 144 × 96 is 24

**(c)** 250 × 28 × 49

**∴** ∛250 × 28 × 49

= ∛5 × 5 × 5 × 2 × 2 × 2 × 7 × 7 × 7

= 5 × 2 × 7

= 70

Thus, the cube root of 250 × 28 × 49 is 70.

**(d)** -216 × 729

**∴** ∛-216 × 729

= ∛- 6 × 6 × 6 × 9 × 9 × 9

= – (6 × 9)

= – 54

Therefore, the cube root of -216 × 729 is -54

**(6) Show that**

**Solution : **

**(a)** As per the question,

∛125 × 216 = ∛125 × ∛216

**∴** L.H.S = 3√125 × 216

= 3√5 × 5 × 5 × 6 × 6 × 6

= 5 × 6

= 30

**∴** R.H.S = 3√125 × 3√216

= 5 × 6

= 30

**∴** L.H.S = R.H.S…(Proved)

**(b)** Given, ∛- 125 × 216 = ∛- 125 × ∛216

**∴** L.H.S, ∛- 125 × 216

= ∛- 27000

= – 30

R.H.S, ∛- 125 × ∛216

= – 5 × 6

= – 30

**∴** L.H.S = R.H.S … [Proved]

**Question no – (7) **

**Solution : **

Given, 2460375 = 3375 × 729

**∴** ∛2460375 = ∛33754 × 729

= ∛15 × 15 × 15 × 9 × 9 × 9

= 15 × 9

= 135

Therefore, the cube root of 24,60,375; 2,03,46,417 and 1, 65,81,375 is 135.

**Question no – (8) **

**Solution : **

**(a) 196**

**∴** 196 = 2 × 2 × 7 × 7

**∴** Multiplied number be = 14

**(b) 3584**

**∴** 3584 = 4 × 4 × 4 × 2 × 2 × 2 × 7

**∴** Multiplied number = 49

**(c) 4116**

**∴ **4116 = 4 × 3 × 7 × 7 × 7

**∴** Multiplied number be 12

**(d) 1275**

**∴** 1275 = 5 × 5 × 17 × 3

**∴** Multiplied number be,

= 5 × 17 × 17 × 9/3.005

**Question no – (9) **

**Solution : **

**(a) 725**

725 = 5 × 5 × 29

**∴** For perfect cube we should divided the number by

= 5 × 5 × 29

= 725

**∴** 3√1 = 1

**(b) 550**

**∴** For divided 5 × 5 × 2 × 11

= 550

**∴** 3√1 = 1

**(c) 1375**

**∴** Divided = 5 × 5 × 3 × 17

= 1375

**∴** 3√1 = 1

**(d) 1824**

1824 = 2 × 2 × 2 × 2 × 2 × 3 × 19

**∴** For perfect cube divided by,

= 2 × 2 × 3 × 19

= 228

**∴** 3√8 = 2

**Question no – (10) **

**Solution :**

In the given question we get,

Cube volume is = 729 cm^{3
}

length of the edge of a cube = ?

Step by Step Solution :

Given volume of the cube is 729 cm^{3}

So now,

Therefore, the length of the edge of the cube will be 9 cm.

**Question no – (11) **

**Solution : **

(2x)^{3} + (3x)^{3} + (4x)^{3} = 33957

8x^{3} + 27x^{3} + 64x^{3} = 33957

99x^{3} = 33957

x^{3} = 33957/99

x = 3√343 = 7

Therefore, the required number are 14, 21 and 28

**Question no – (12) **

**Solution : **

Let the length of cube is = a

**∴** 6a^{2} = 726

**∴** a^{2} = 121

**∴** a = 11

**∴ Volume,**

= 11 × 11 × 11

= 1331 m^{3}

Therefore, the Volume will be 1331 m^{3}

**Question no – (13) **

**Solution : **

**(a)** ∛64 + ∛.512 – ∛0.125

= 8 + 3√512/100 – 3√125/100

= 8 + 8/10 – 5/10

= 8 + 3/10

= 8 + .3

= 8.3…(Simplified)

**(b)** ∛729/216 × 2

= 9/16 × 2

= 3…(Simplified)

**(c)** ∛0.008/0.125 + √0.16/0.09 – 2

= 2/5 + 4/3 – 2

= 6 + 20 – 30/15

= – 4/15…(Simplified)

**Previous Chapter Solution : **