How do you simplify sqrt8/(2sqrt7)?

Apr 14, 2018

$\frac{\sqrt{14}}{7}$

Explanation:

$\frac{\sqrt{8}}{2 \sqrt{7}}$

$\frac{\sqrt{4 \cdot 2}}{2 \sqrt{7}}$

$\frac{\sqrt{4} \cdot \sqrt{2}}{2 \sqrt{7}}$

$\frac{2 \sqrt{2}}{2 \sqrt{7}}$

Since both the numerator and denominator is multiplied by $2$, we can cancel $2$:
$\frac{\textcolor{red}{\cancel{2}} \sqrt{2}}{\textcolor{red}{\cancel{2}} \sqrt{7}}$

And what's left is:
$\frac{\sqrt{2}}{\sqrt{7}}$

If you need to simplify it further, you can rationalize the denominator by multiplying the whole expression by $\sqrt{7}$:
$\frac{\sqrt{2}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Which becomes:
$\frac{\sqrt{14}}{7}$

Hope this helps!