How do you simplify sqrt (2 / 25) + sqrt (8 / 9)?

Apr 29, 2018

Answer:

$\frac{\sqrt{2}}{5} + \frac{2 \sqrt{2}}{3}$

Explanation:

$\sqrt{\frac{2}{25}} + \sqrt{\frac{8}{9}}$

Simplify the denominators:
$\frac{\sqrt{2}}{5} + \frac{\sqrt{8}}{3}$

Simplify $\sqrt{8}$:
$\frac{\sqrt{2}}{5} + \frac{\sqrt{4 \cdot 2}}{3}$

$\frac{\sqrt{2}}{5} + \frac{\sqrt{4} \cdot \sqrt{2}}{3}$

$\frac{\sqrt{2}}{5} + \frac{2 \sqrt{2}}{3}$

Hope this helps!

Apr 30, 2018

Answer:

$\textcolor{b l u e}{\frac{13 \sqrt{2}}{15}}$

Explanation:

$\sqrt{\frac{2}{25}} = \frac{\sqrt{2}}{5}$

$\sqrt{\frac{8}{9}} = \frac{\sqrt{8}}{3}$

$\sqrt{8} = 2 \sqrt{2}$

$\therefore$

$\frac{\sqrt{2}}{5} + \frac{2 \sqrt{2}}{3}$

Add:

$\frac{3 \sqrt{2} + 10 \sqrt{2}}{15} = \frac{13 \sqrt{2}}{15}$