# How do you simplify 4sqrt8 - 3 sqrt2?

Jul 13, 2016

$5 \sqrt{2}$

#### Explanation:

Note that $8 = 2 \times 4 = 2 \times {2}^{2}$

So we have

$4 \sqrt{2 \times \textcolor{red}{{2}^{2}}} - 3 \sqrt{2}$

Take the $\textcolor{red}{{2}^{2}}$ outside the root making it just $\textcolor{b l u e}{2}$

$4 \times \textcolor{b l u e}{2} \sqrt{2} - 3 \sqrt{2} \text{ "=" } 8 \sqrt{2} - 3 \sqrt{2}$

$\textcolor{w h i t e}{. .}$
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Think about $8 a - 3 a = 5 a$

Instead of $a$ we have $\sqrt{2}$ but the same process applies.
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$\textcolor{w h i t e}{. .}$

$8 \sqrt{2} - 3 \sqrt{2} = 5 \sqrt{2}$