# How do you simplify root7(640 )?

Dec 23, 2016

$\sqrt[7]{640} = 2 \sqrt[7]{5}$

#### Explanation:

There are a couple of properties that hold for any $n$th root (where $n$ is a positive integer), including $7$th roots:

$\sqrt[n]{a b} = \sqrt[n]{a} \sqrt[n]{b} \text{ }$ when $a , b \ge 0$

$\sqrt[n]{{a}^{n}} = a \text{ }$ when $a \ge 0$

Factorising $640$, we find:

$640 = {2}^{7} \cdot 5$

So:

$\sqrt[7]{640} = \sqrt[7]{{2}^{7} \cdot 5} = \sqrt[7]{{2}^{7}} \cdot \sqrt[7]{5} = 2 \sqrt[7]{5}$