# How do you simplify 200/sqrt5?

Mar 10, 2018

The result is $40 \sqrt{5}$.

#### Explanation:

Factor $200$, separate the fraction, then combine the exponents:

$\frac{\textcolor{b l u e}{200}}{\sqrt{5}}$

$\frac{\textcolor{b l u e}{200}}{{5}^{\frac{1}{2}}}$

$\textcolor{b l u e}{200} \cdot \frac{1}{{5}^{\frac{1}{2}}}$

$\textcolor{b l u e}{200} \cdot {5}^{- \frac{1}{2}}$

$\textcolor{b l u e}{40 \cdot 5} \cdot {5}^{- \frac{1}{2}}$

$\textcolor{b l u e}{40 \cdot {5}^{1}} \cdot {5}^{- \frac{1}{2}}$

$\textcolor{b l u e}{40} \cdot {5}^{1 - \frac{1}{2}}$

$\textcolor{b l u e}{40} \cdot {5}^{\frac{1}{2}}$

$\textcolor{b l u e}{40} \cdot \sqrt{5}$

$\textcolor{b l u e}{40} \sqrt{5}$