Question

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

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

Answer 1

(1) Prime facorisation of 64 is :

64 = $2\times 2\times 2\times 2\times 2\times 2=2^3\times 2^3\therefore \sqrt[3]{364}=2\times 2=4$
The cube root of 64 = 4

(2) Prime factorisation of 512, is

512 = $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^3\times 2^3\times 2^3\therefore \sqrt[3]{3512}=2\times 2\times 2=8$
Thus, the cube root of 512 = 8

(3) Prime factorisation of 10648, is :


10648 = $2\times 2\times 2\times 11\times 11\times 11=2^3\times {11}^3\therefore \sqrt[3]{310648}=2\times 11=22$
Thus, the cube root of 10648 = 22.

(4) Prime factorisation of 27000, is:


27000 = $2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5=2^3\times 3^3\times 5^3\therefore \sqrt[3]{327000}=2\times 3\times 5=300.$
Thus, the cube root of 27000 = 300.