from a handpicked tutor in LIVE 1-to-1 classes

# Find the cube root of each of the following numbers by prime factorization method.

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

(vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616

(x) 91125

**Solution:**

To find the cube root of a number, the factors in the prime factorization of the number should be grouped as triplets.

(i) 64

64 = 2 × 2 × 2 × 2 × 2 × 2

= 2^{3} × 2^{3}

∛64 = 2 × 2 = 4

(ii) 512

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2^{3} × 2^{3} × 2^{3}

∛512 = 2 × 2 × 2 = 8

(iii) 10648

10648 = __2 × 2 × 2 × 11 × 11 × 11__

= 2^{3} × 11^{3}

∛10648 = 2 × 11 = 22

(iv) 27000

27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5

= 2^{3} × 3^{3} × 5^{3}

∛27000 = 2 × 3 × 5 = 30

(v) 15625

15625 = 5 × 5 × 5 × 5 × 5 × 5

= 5^{3} × 5^{3}

∛15625 = 5 × 5 = 25

(vi) 13824

13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

= 2^{3} × 2^{3} × 2^{3} × 3^{3}

∛13824 = 2 × 2 × 2 × 3 = 24

(vii) 110592

110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × __3 __× 3 × 3

= 2^{3} × 2^{3} × 2^{3} × 2^{3} × 3^{3}

∛110592 = 2 × 2 × 2 × 2 × 3 = 48

(viii) 46656

46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

= 2^{3} × 2^{3} × 3^{3} × 3^{3}

∛46656 = 2 × 2 × 3 × 3 = 36

(ix) 175616

175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7

= 2^{3} × 2^{3} × 2^{3} × 7^{3}

∛175616 = 2 × 2 × 2 × 7 = 56

(x) 91125

91125 = 5 × 5 × 5 × 3 × 3 × 3 × 3 × 3 × 3

= 5^{3} × 3^{3} × 3^{3}

∛91125 = 5 × 3 × 3 = 45

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 7

**Video Solution:**

## Find the cube root of each of the following numbers by prime factorization method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125

NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 Question 1

**Summary:**

The cube root of each of the following numbers by prime factorization method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125 are (i) 4, (ii) 8, (iii) 22, (iv) 30, (v) 25, (vi) 24, (vii) 48, (viii) 36, (ix) 56, (x) 45

**☛ Related Questions:**

- 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.
- 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.
- Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.(i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704.
- Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

visual curriculum