# How do you simplify sqrt(27su^3) ?

Aug 23, 2016

$3 u \sqrt{3 s u}$

#### Explanation:

Write the numbers under the root sign as prime factors, or try to form even powers.

$\sqrt{27 s {u}^{3}} = \sqrt{3 \times \textcolor{red}{{3}^{2}} \times s \times u \times \textcolor{red}{{u}^{2}}}$

=$\textcolor{red}{3 u} \sqrt{3 s u}$

Note that this assumes $u \ge 0$

For a general solution:

$3 | u | \sqrt{3 s u}$