# How do you get rid of the square root sign in \sqrt { 147m ^ { 3} n ^ { 3} }?

Mar 20, 2018

${\left(147\right)}^{\frac{1}{2}} {m}^{\frac{3}{2}} {n}^{\frac{3}{2}}$

#### Explanation:

$\textcolor{b l u e}{\sqrt{{a}^{n}} = {a}^{\frac{n}{2}}}$

$\sqrt{147 {m}^{3} {n}^{3}} = {\left(147\right)}^{\frac{1}{2}} {m}^{\frac{3}{2}} {n}^{\frac{3}{2}}$

If you want to simplify:

$= {\left(3 \cdot 49\right)}^{\frac{1}{2}} {m}^{\frac{3}{2}} {n}^{\frac{3}{2}}$

$= 7 {\left(3\right)}^{\frac{1}{2}} {\left(m n\right)}^{\frac{3}{2}}$