# What is the square root of 10 times the square root of 20?

Sep 9, 2015

$10 \sqrt{2}$

#### Explanation:

You need to multiply $\sqrt{10}$ and $\sqrt{20}$.

Before doing that, take a look at $\sqrt{20}$. Notice that you can write it as

$\sqrt{20} = \sqrt{2 \cdot 10}$

If you use the product property of radicals, which tells you that

$\textcolor{b l u e}{\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}}$

you can write

$\sqrt{2 \cdot 10} = \sqrt{2} \cdot \sqrt{10}$.

$\sqrt{10} \cdot \sqrt{2} \cdot \sqrt{10} = \sqrt{2} \cdot \sqrt{10} \cdot \sqrt{10}$
$= \sqrt{2} \cdot \sqrt{10 \cdot 10} = \sqrt{2} \cdot \sqrt{100}$
$= \sqrt{2} \cdot 10 = \textcolor{g r e e n}{10 \sqrt{2}}$