Frank Learning Maths Class 8 Chapter 4 Cubes and Cube Roots Exercise 4.2 Solutions

Frank Learning Maths Class 8 Chapter 4 Cubes and Cube Roots Exercise 4.2 Solutions

This post is created to help all the CBSE Class 8 students for the Solutions of Frank Learning Maths Class 8 Mathematics Book, Chapter 4 Cubes and Cube Roots Exercise 4.2. Here students can easily find step by step solutions of all the problems for Cubes and Cube Roots Exercise 4.2. Step by Step proper solutions for every problems. All the problem are solved with easily understandable methods with proper guidance so that all the students can understand easily.

Chapter 4 – Cubes and Cube Roots

Cubes and Cube Roots – Exercise 4.2 all Questions Solution

(1) Evaluate 

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

(2) Find the cube root of the following by finding the units and the tens digits

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

(3) Find the cube root of the following by prime factorisation

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

(4) Find the cube root of the following rational and decimals. 

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

(5) Find the cube root of the following

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 cm³

length of the edge of a cube = ?

Step by Step Solution :

Given volume of the cube is 729 cm³

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

8x³ + 27x³ + 64x³ = 33957

99x³ = 33957

x³ = 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

∴ 6a² = 726

∴ a² = 121

∴ a = 11

∴ Volume,

= 11 × 11 × 11

= 1331 m³

Therefore, the Volume will be 1331 m³

Question no – (13) Simplify

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)