# How do you simplify sqrt45/(4sqrt81)?

Mar 15, 2016

$\frac{\sqrt{5}}{12}$

#### Explanation:

$1$. Start by multiplying the numerator and denominator by $\frac{\sqrt{81}}{\sqrt{81}}$ to get rid of the radical in the denominator. Note that the value of the fraction would not change since $\frac{\sqrt{81}}{\sqrt{81}} = 1$.

$\frac{\sqrt{45}}{4 \sqrt{81}}$

$= \frac{\sqrt{45}}{4 \sqrt{81}} \left(\frac{\sqrt{81}}{\sqrt{81}}\right)$

$2$. Simplify.

$= \frac{\sqrt{45 \cdot 81}}{4 \left(\sqrt{81} \sqrt{81}\right)}$

$= \frac{\sqrt{3645}}{4 \left(81\right)}$

$= \frac{\sqrt{3645}}{324}$

$3$. Using a perfect square, break down the radical in the numerator.

$= \frac{\sqrt{{27}^{2} \cdot 5}}{324}$

$4$. Simplify.

$= \frac{27 \sqrt{5}}{324}$

$= \frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{27}}}}^{1} \sqrt{5}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{324}}}} ^ 12$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \frac{\sqrt{5}}{12} \textcolor{w h i t e}{\frac{a}{a}} |}}}$