# How do you simplify 2 sqrt20 - 3 sqrt 7- 2 sqrtt 5 + 4 sqrt 63?

Jan 15, 2018

$2 \sqrt{5} + 9 \sqrt{7}$

#### Explanation:

I am presuming that there is a typo in the third term where instead of $- 2 \sqrt{5}$, you have typed a double $t$ to get $- 2 \sqrt{t} 5$.

Using that presumption, I shall calculate the above as:

$2 \sqrt{20} - 3 \sqrt{7} - 2 \sqrt{5} + 4 \sqrt{63}$

Reduce the first and the last terms by first factorising and then removing the squares from under the square root sign.

$2 \sqrt{2 \times 2 \times 5} - 3 \sqrt{7} - 2 \sqrt{5} + 4 \sqrt{3 \times 3 \times 7}$

$2 \times 2 \sqrt{5} - 3 \sqrt{7} - 2 \sqrt{5} + 4 \times 3 \sqrt{7}$

$4 \sqrt{5} - 3 \sqrt{7} - 2 \sqrt{5} + 12 \sqrt{7}$

Rearrange with the preceding signs to put like terms together.

$4 \sqrt{5} - 2 \sqrt{5} + 12 \sqrt{7} - 3 \sqrt{7}$

$\left(4 \sqrt{5} - 2 \sqrt{5}\right) + \left(12 \sqrt{7} - 3 \sqrt{7}\right)$

$2 \sqrt{5} + 9 \sqrt{7}$

If I have erred in my original presumption, this answer will not apply. :)