Question

Using prime factorisation, find the cube roots of 512

Answer 1

First we have to find out the factors by using prime factorisation method.

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

So, prime factors of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Now, grouping the prime factors = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)

Then, cube root of `512 = root(3)(512)`

= `root(3)((2 xx 2 xx 2) xx (2 xx 2 xx 2) xx (2 xx 2 xx 2))`

= `root(3)(2^3 xx 2^3 xx 2^3)`

= 2 × 2 × 2

= 8

∴ The cube root of 512 is 8.