# How do you simplify sqrt6 (sqrt3 + 5 sqrt2)?

Mar 21, 2018

$10 \sqrt{3} + 3 \sqrt{2}$
You must distribute the $\sqrt{6}$

#### Explanation:

Radicals can be multiplied, no matter the value under the sign.
Multiply $\sqrt{6} \cdot \sqrt{3}$, which equals $\sqrt{18}$.
$\sqrt{18}$$\to$$\left(\sqrt{9 \cdot 2}\right)$$\to$$3 \sqrt{2}$ ($\sqrt{9} = 3$)
$\sqrt{6} \cdot 5 \sqrt{2} = 5 \sqrt{12}$$\to$$5 \cdot \sqrt{3 \cdot 4}$
$\sqrt{4} = 2$ $\to$$5 \cdot 2 \sqrt{3} = 10 \sqrt{3}$
Hence, $10 \sqrt{3} + 3 \sqrt{2}$