# How do you simplify 5 square root of 243?

Mar 20, 2018

The simplified radical is $45 \sqrt{3}$.

#### Explanation:

First, we need to write the English statement in "math form":

${\overbrace{\text{5"^(5xx) overbrace"square root of"^(sqrtcolor(white)x) overbrace"243}}}^{\quad 243 \quad}$

To simplify this, factor $243$ into some square numbers that we know:

$\textcolor{w h i t e}{=} 5 \times \sqrt{243}$

$= 5 \times \sqrt{\textcolor{red}{81} \cdot 3}$

$= 5 \times \sqrt{\textcolor{red}{{9}^{2}} \cdot 3}$

$= 5 \times \textcolor{red}{9} \times \sqrt{3}$

$= 45 \times \sqrt{3}$

$= 45 \sqrt{3}$

This is the simplified radical. Hope this helped!