# How do you simplify 4 times the square root of 8 over the square root of 2?

Jul 23, 2018

color(purple)(=> 4 * 2 = 8

#### Explanation:

$\frac{4 \cdot \sqrt{8}}{\sqrt{2}}$

$\implies \frac{4 \cdot \sqrt{2 \cdot 2 \cdot 2}}{\sqrt{2}}$

$\implies \frac{4 \cdot \sqrt{4} \cdot \cancel{\sqrt{2}}}{\cancel{\sqrt{2}}}$

$\implies 4 \cdot \sqrt{4}$

color(purple)(=> 4 * 2 = 8

Jul 23, 2018

8

#### Explanation:

Breaking the question down into its component parts.

4 times" "..................................." "4xx?

the square root of 8$\text{ "................." } 4 \times \sqrt{8}$

over the square root of 2$\text{ "..........." } 4 \times \frac{\sqrt{8}}{\sqrt{2}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Did you know you can write this like: $4 \times \sqrt{\frac{8}{2}}$

It has exactly the same value. Test it with a calculator.

$4 \times \sqrt{4}$

$4 \times 2 = 8$

Jul 23, 2018

$8$

#### Explanation:

We have the following:

$\frac{4 \cdot \sqrt{8}}{\sqrt{2}}$

We can start by rationalizing the denominator. We can multiply this expression by $\frac{\sqrt{2}}{\sqrt{2}}$ to get

$\frac{4 \sqrt{8} \sqrt{2}}{2}$

Recall that $\sqrt{a} \sqrt{b} = \sqrt{a b}$. With this in mind, we can condense the radicals as

$\frac{4 \sqrt{16}}{2} = \frac{4 \cdot {\cancel{4}}^{2}}{\cancel{2}} = 4 \cdot 2 = \textcolor{b l u e}{8}$

Our expression simplifies to $8$.

Hope this helps!