Question

What is the 6th root of 256? ...left in radical notation

Answer 1

First of all we would break 256 into its simple factors.

2 / 256
2 / 128
2 / 64
2 / 32
2 / 16
2 / 8
2 / 4
2 / 2
1.

Therefore 256 = 2 * 2 * 2 * 2 *2 * 2 * 2 *2

Therefore sixth root of 256 =
`\sqrt[6]{2*2*2*2*2*2*2*2}`

For every six 2s we bring out one out of the root.

=
`2\sqrt[6]{2*2}`

=
`2\sqrt[6]{4}`

That's our answer.