# How do you simplify sqrt(343/280)?

Mar 21, 2017

$\sqrt{\frac{343}{280}} = \frac{7 \sqrt{10}}{20}$

#### Explanation:

First pull out as many perfect squares as possible:

$\sqrt{\frac{343}{280}} = \sqrt{\frac{\textcolor{red}{7} \cdot \textcolor{red}{7} \cdot 7}{\textcolor{b l u e}{2} \cdot \textcolor{b l u e}{2} \cdot 2 \cdot 7 \cdot 5}} = \frac{\textcolor{red}{7}}{\textcolor{b l u e}{2}} \sqrt{\frac{7}{2 \cdot 7 \cdot 5}}$

Next, cancel out any terms left inside the radical and simplify.

$\frac{7}{2} \sqrt{\frac{\cancel{7}}{2 \cdot \cancel{7} \cdot 5}} = \frac{7}{2} \sqrt{\frac{1}{10}} = \frac{7}{2 \sqrt{10}}$

Now, multiply both the numerator and denominator by $\sqrt{10}$ to rationalize the denominator.

$\frac{7}{2 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}} = \frac{7 \sqrt{10}}{2 \cdot 10} = \frac{7 \sqrt{10}}{20}$