# How do you simplify sqrt(h^11)?

May 16, 2016

$\sqrt{{h}^{11}} = \textcolor{b l u e}{{h}^{5} \sqrt{h}}$

#### Explanation:

$\sqrt{{h}^{11}} = \sqrt{{h}^{10} \cdot h}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{\left({h}^{5}\right)}^{2} \cdot h}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{\left({h}^{5}\right)}^{2}} \cdot \sqrt{h}$

$\textcolor{w h i t e}{\text{XXX}} = {h}^{5} \sqrt{h}$

May 16, 2016

${h}^{5} \sqrt{h}$

#### Explanation:

The 'long way round' method to fully explain what is happening.

$\sqrt{{h}^{11}} = \sqrt{{h}^{2} \times {h}^{2} \times {h}^{2} \times {h}^{2} \times {h}^{2} \times h}$

There are 5 lots of $\times {h}^{2}$ so by taking the square root of them we have 5 lots of $\times h$ giving ${h}^{5}$

${h}^{5} \sqrt{h}$