**Download NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 – Cube and Cube roots**

**NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 – Cube and Cube roots, has been designed by the NCERT to test the knowledge of the student on the topic – Cube Roots**

- Cube root through prime factorisation method
- Cube root of a cube number

**1. Find cube root of each of the following numbers by prime factorisation method.**

**(i) 64
(ii) 512
(iii) 10648
(iv) 27000
(v) 15625
(vi) 13824
**

**(vii) 110592**

(viii) 46656

(ix) 175616

(x) 91125

(viii) 46656

(ix) 175616

(x) 91125

**Solution:**

**(i)** Prime factorisation of 64

64 = __2 × 2 × 2__ × __2 × 2 × 2
__Therefore, cube root of 64 = 2 × 2 = 4

**(ii)** Prime factorisation of 512

512 = __2 × 2 × 2__ × __2 × 2 × 2__ × __2 × 2 × 2
__Therefore, cube root of 512 = 2×2×2 = 8

**(iii)** Prime factorisation of 10648

10648 = __2 × 2 × 2__ × __11 × 11 × 11
__Therefore, cube root of 10648 = 2×11 = 22

**(iv)** Prime factorisation of 27000

27000 = __2 × 2 × 2__ × __3 × 3 × 3__ × __5 × 5 × 5
__Therefore, cube root of 27000 = 2×3×5 = 30

**(v)** Prime factorisation of 15625

15625 = __5 × 5 × __5 × 5__ × 5 × 5
__Therefore, cube root of 15625 = 5×5 = 25

**(vi)** Prime factorisation of 13824

13824 = __2 × 2 × 2__ × __2 × 2 × 2__ × __2 × 2 × 2__ × __3 × 3 × 3
__Therefore, cube root of 13824 = 2×2×2×3 = 24

**(vii)** Prime factorisation of 110592

110592 = __2 × 2 × 2__ × __2 × 2 × 2__ × __2 × 2 × 2__ × __2 × 2 × 2__ × __3 × 3 × 3
__Therefore, 110592 = 2×2×2×2×3 = 48

**(viii)** Prime factorisation of 46656

46656 = __2 × 2 × 2__ × __2 × 2 × 2__ × __3 × 3 × 3__ × __3 × 3 × 3
__Therefore, cube root of 46656 = 2×2×3×3 = 36

**(ix)** Prime factorisation of 175616

175616 = __2 × 2 × 2__ × __2 × 2 × 2__ × __2 × 2 × 2__ × __7 × 7 × 7
__Therefore, cube root of 175616 = 2×2×2×7 = 56

**(x)** Prime factorisation of 91125

91125 = __3 × 3 × 3__ × __3 × 3 × 3__ × __5 × 5 × 5
__Therefore, cube root of 91125 = 3×3×5 = 45

**Q.2 State true or false.**

**(i) Cube of any odd number is even.
**

**(ii) A perfect cube does not end with two zeros.**

**(iii) If square of a number ends with 5, then its cube ends with 25.**

**(iv) There is no perfect cube which ends with 8.**

**(v) The cube of a two-digit number may be a three-digit number.**

**(vi) The cube of a two-digit number may have seven or more digits.**

**(vii) The cube of a single digit number may be a single digit number.**

**Solution:**

**(i)** False

Explanation: Cube of any odd number will be an odd number, when we multiply three times an odd number the product will be an odd number.

**(ii)** True

Explanation: Perfect cube will end with triples of zeros

**(iii)** False

Explanation: It is not necessary

Example:

square of 15 is 225

cube of 15 is 3375 ( not ending with 25 )

**(iv)** False

Explanation: The cubes of all the numbers having their unit’s place digit as 2 will end with 8

**(v)** False

Explanation: Cube of smallest 2-digit number, 10 is 1000 which has 4 digits

**(vi)** False

Explanation: Cube of largest 2-digit number, 99 is 970277 which has 6 digits

**(vii)** True

Explanation: Cube of 1 and Cube of 2 are single digit numbers

**Q.3 You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.**

**Solution:**

**Cube root of 1331:**

Step 1:

making groups of three digits starting from the right most digit of the number.

1 331

Step 2:

first group 331 ends with 1 so the unit’s place digit of the cube root is 1

second group has only one-digit, 1, which gives the ten’s place digit of cube root as 1

Therefore, cube root of 1331 is 11

**Cube root of 4913:**

Step 1:

making groups of three digits starting from the right most digit of the number.

4 913

Step 2:

first group 913 ends with 3 so the unit’s place digit of the cube root is 7

second group has only one-digit, 4

1^{3} = 1 and 2^{3} = 8, 1 < 4 < 8

which gives the ten’s place digit of cube root as 1

Therefore, cube root of 1913 is 17

**Cube root of 12167**

Step 1:

making groups of three digits starting from the right most digit of the number.

12 167

Step 2:

first group 167 ends with 7 so the unit’s place digit of the cube root is 3

second group 12

2^{3} = 8 and 3^{3} = 27, 8 < 12 < 27

which gives the ten’s place digit of cube root as 2

Therefore, cube root of 12167 is 23

**Cube root of 32768**

Step 1:

making groups of three digits starting from the right most digit of the number.

32 768

Step 2:

first group 768 ends with 8 so the unit’s place digit of the cube root is 2

second group 32

3^{3} = 27 and 4^{3} = 64, 27 < 32 < 64

which gives the ten’s place digit of cube root as 3

Therefore, cube root of 32768 is 32

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.1 – Comparing Quantities can be accessed by clicking here**

**Download NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2**

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