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) 64(ii) 512(iii) 10648(iv) 27000(v) 15625
Answer» (i) Prime factorisation of 64 = 2 x 2 x 2 x 2 x 2 x 2 ∴ 3√64 = 2 x 2 = 4 (ii) Prime factorisation of 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 ∴ 3√512 = 2 x 2 x 2 = 8 (iii) Prime factorisation of 10648 = 2 x 2 x 2 x 11 x 11 x 11 ∴ 3√10648 = 2 x 11 = 22 (iv) Prime factorisation of 27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 ∴ 3√27000 = 2 x 3 x 5 = 30 (v) Prime factorisation of 15625 = 5 x 5 x 5 x 5 x 5 x 5 ∴ 3√15625 = 5 x 5 = 25

Find the cube root of each of the following numbers by prime factorisation method.(i) 64(ii) 512(iii) 10648(iv) 27000(v) 15625

Answer»

(i) Prime factorisation of 64 = 2 x 2 x 2 x 2 x 2 x 2

∴ 3√64 = 2 x 2 = 4

(ii) Prime factorisation of 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

∴ 3√512 = 2 x 2 x 2 = 8

(iii) Prime factorisation of 10648 = 2 x 2 x 2 x 11 x 11 x 11

∴ 3√10648 = 2 x 11 = 22

(iv) Prime factorisation of 27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

∴ 3√27000 = 2 x 3 x 5 = 30

(v) Prime factorisation of 15625 = 5 x 5 x 5 x 5 x 5 x 5

∴ 3√15625 = 5 x 5 = 25