Question

How do you find the value of 3 square root of 125?

Answer 1

`3 xx sqrt125 = 15sqrt5` and `root(3)125 = 5`

Explanation:

I have heard many students read `root(3)n` as "the third square root of n". This is a mistake. The square root is `root(2)n` (usually denoted `sqrtx`), the third (or cube) root is `root(3)n`, the fourth root is `root(4)n` and so on.

Whichever was meant the first step for simplifying is the same. Factor the radicand (the thing under the root symbol)

`125 = 5xx25 = 5xx5xx5 = 5^3`

so

`3sqrt125 =3 xx sqrt (25xx5) = 3xx sqrt25 xx sqrt5 = 3xx5xx sqrt5 = 15sqrt5`

And

`root(3)125 = root(3) (5^3) = 5`