# Frank Learning Maths Class 8 Solutions Chapter 4

## 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

= – (133/183)

= 2196/5832

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

(b) 27/32

(27/32)3

= 273/323

= 19683/32768

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

(c) 2 3/11

(25/11)3

= 253/113

= 15625/1331

So, the cube of 2 3/11 is 15625/1331

(d) -1 5/8

-133/83

= – 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) 73 = 43 + 45 + 47 + 49 + 51 + 53 + 55

(b) 8= 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71

(c) 10= 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 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)

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)

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Updated: June 5, 2023 — 7:05 am