# How do you simplify sqrt2(sqrt6+sqrt10)?

Jan 24, 2017

Radicals can be multiplied together as long as they are all under the same "root" , like square roots, cube roots, or other roots.

#### Explanation:

I would expand by Distributing:
$\sqrt{2} \cdot \sqrt{6} + \sqrt{2} \cdot \sqrt{10}$
= $\sqrt{2} \sqrt{2} \sqrt{3} + \sqrt{2} \sqrt{2} \sqrt{5}$
and look for "pairs" of matching roots.
=$\sqrt{{2}^{2}} \sqrt{3} + \sqrt{{2}^{2}} \sqrt{5}$ (you could even skip this step)
= $2 \sqrt{3} + 2 \sqrt{5}$.

Pairs of roots that are the same factor simplify easily:
$\sqrt{93} \sqrt{93} = 93$ every time!!