# How do you simplify 20sqrt10+12+(-75sqrt2)-9sqrt5 ?

Oct 8, 2015

$3 \cdot \left(4 - 3 \sqrt{5}\right) + 5 \sqrt{2} \cdot \left(4 \sqrt{5} - 15\right)$

#### Explanation:

Your starting expression looks like this

$20 \sqrt{10} + 12 - 75 \sqrt{2} - 9 \sqrt{5}$

Right from the start, you can say that $12$, the only term that doesn't have a radical attached, will remain by itself.

As far as the other terms are concerned, you don't really have that much elbow room. You could try to write $10 = 2 \cdot 5$ and get

$20 \sqrt{10} = 20 \sqrt{2 \cdot 5} = 20 \cdot \sqrt{2} \cdot \sqrt{5}$

Now you could use $5 \sqrt{2}$ as a common factor to write

$12 + 5 \sqrt{2} \cdot \left(4 \sqrt{5} - 15\right) - 9 \sqrt{5}$

Now you could maybe use $3$ as a common factor between $12$ and $9 \sqrt{5}$ to get

$3 \cdot \left(4 - 3 \sqrt{5}\right) + 5 \sqrt{2} \cdot \left(4 \sqrt{5} - 15\right)$