Question

Find the cube root of the following number by the prime factorisation method.

512

Answer 1

2	512
2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

Prime factorisation of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2³ × 2³ × 23 = (2 × 2 × 2)³

∴ `root3 512` = 2 × 2 × 2

= 8