# How do you simplify sqrt8(5 sqrt 2 - sqrt 18)?

Feb 24, 2016

First, notice that $\sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}$

Also, notice that $\sqrt{18} = \sqrt{9 \cdot 2} = 3 \sqrt{2}$

Now we have $2 \sqrt{2} \left(5 \sqrt{2} - 3 \sqrt{2}\right)$

We can just subtract inside the parenthesis

Treating the radicals as variables, just subtract and get $2 \sqrt{2}$

Now we have $2 \sqrt{2} \cdot 2 \sqrt{2}$

$2 \cdot 2 = 4$
$\sqrt{2} \cdot \sqrt{2} = {\sqrt{2}}^{2} = 2$
And finally, just multiply to get $2 \cdot 4 = 8$