# Question #b1685

Dec 14, 2016

$\sqrt{8} \cdot \sqrt{20}$

$= \sqrt{{2}^{2} \cdot 2} \cdot \sqrt{{2}^{2} \cdot 5}$

$= 2 \sqrt{2} \cdot 2 \sqrt{5}$

$= 4 \sqrt{2 \cdot 5}$

$= 4 \sqrt{10}$

Dec 14, 2016

$4 \sqrt{10}$

#### Explanation:

Since sometimes students have trouble with exponents, another way to look at this question is to factor the number under the radical where one of the factors is a perfect square.
$\sqrt{8} \cdot \sqrt{20} = \sqrt{4 \cdot 2} \cdot \sqrt{4 \cdot 5}$
$\textcolor{w h i t e}{a a a a a a a a} = \sqrt{4} \sqrt{2} \cdot \sqrt{4} \sqrt{5}$
$\textcolor{w h i t e}{a a a a a a a a} = 2 \sqrt{2} \cdot 2 \sqrt{5}$
Then multiply the coefficients together separately and the numbers under the roots separately.
$\textcolor{w h i t e}{a a a a a a a a a} = \left(2\right) \left(2\right) \sqrt{2 \cdot 5}$
$\textcolor{w h i t e}{a a a a a a a a a} = 4 \sqrt{10}$