# How do you simplify sqrt2 + sqrt( 2/49)?

May 9, 2018

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

#### Explanation:

$\sqrt{2}$ has no perfect squares in it, so we can leave it the way it is for now. But we can rewrite this entire expression as

$\sqrt{2} + \left(\frac{\sqrt{2}}{\sqrt{49}}\right)$

(because of the property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$)

Which simplifies to

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

We can factor out a $\sqrt{2}$ to get

$\sqrt{2} \left(1 + \frac{1}{7}\right)$

$= \sqrt{2} \left(1 \frac{1}{7}\right)$

Changing to an improper fraction to get

$= \sqrt{2} \left(\frac{8}{7}\right)$

which finally simplifies to

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

Hope this helps!