# How do you multiply sqrt5^6?

Sep 25, 2015

It is 125

#### Explanation:

You can calculate this in (at least) 2 ways:

1) ${\sqrt{5}}^{6} = \left(\sqrt{5} \sqrt{5}\right) \left(\sqrt{5} \sqrt{5}\right) \left(\sqrt{5} \sqrt{5}\right) = 5 \cdot 5 \cdot 5 = 125$

2)
You can use the laws of power operations

• Write $\sqrt{5}$ as ${5}^{\frac{1}{2}}$ to get: ${\sqrt{5}}^{6} = {\left({5}^{\frac{1}{2}}\right)}^{6}$
• Use the law that: ${\left({a}^{b}\right)}^{c} = {a}^{b \cdot c}$ to get:
${\left({5}^{\frac{1}{2}}\right)}^{6} = {5}^{\frac{1}{2} \cdot 6} = {5}^{3} = 125$