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

Sep 9, 2015

$3 \times \sqrt{125} = 15 \sqrt{5}$ and $\sqrt[3]{125} = 5$

#### Explanation:

I have heard many students read $\sqrt[3]{n}$ as "the third square root of n". This is a mistake. The square root is $\sqrt[2]{n}$ (usually denoted $\sqrt{x}$), the third (or cube) root is $\sqrt[3]{n}$, the fourth root is $\sqrt[4]{n}$ and so on.

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

$125 = 5 \times 25 = 5 \times 5 \times 5 = {5}^{3}$

so

$3 \sqrt{125} = 3 \times \sqrt{25 \times 5} = 3 \times \sqrt{25} \times \sqrt{5} = 3 \times 5 \times \sqrt{5} = 15 \sqrt{5}$

And

$\sqrt[3]{125} = \sqrt[3]{{5}^{3}} = 5$