Find the cube root of each of the following numbers by prime factorisa

1.	Find the cube root of each of the following numbers by prime factorisation method.(i) 13824(ii) 110592(iii) 46656
Answer» (i) Prime factorisation of 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2x 3 x 3 x 3 ∴ 3√13824 = 2 x 2 x 2 x 3 = 24 (ii) Prime factorisation of 110592 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 ∴ 3√110592 = 2 x 2 x 2 x 2 x 3 = 48 (iii) Prime factorisation of 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x3 x 3 ∴ 3√46656 = 2 x 2 x 3 x 3 = 36

Find the cube root of each of the following numbers by prime factorisation method.(i) 13824(ii) 110592(iii) 46656

Answer»

(i) Prime factorisation of 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2x 3 x 3 x 3

∴ 3√13824 = 2 x 2 x 2 x 3 = 24

(ii) Prime factorisation of 110592 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

∴ 3√110592 = 2 x 2 x 2 x 2 x 3 = 48

(iii) Prime factorisation of 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x3 x 3

∴ 3√46656 = 2 x 2 x 3 x 3 = 36