# How do you combine 4sqrt20-sqrt45+7sqrt5?

Oct 13, 2015

Answer is 12$\sqrt{5}$

#### Explanation:

$4 \sqrt{20} - \sqrt{45} + 7 \sqrt{5}$ equation 1

The equation has to be simplyfied such that the number in the square root be same for all the terms in the equation. Last term in the equation can not simplified further, hence number in the square root 5.

$\sqrt{20} = \sqrt{4 \times 5}$ = $\sqrt{2 \times 2 \times 5}$ =2$\sqrt{5}$

$\sqrt{45} = \sqrt{9 \times 5}$ = $\sqrt{3 \times 3 \times 5}$ = 3$\sqrt{5}$

substitute these values in the equation 1

$4 \times 2 \sqrt{5} - 3 \sqrt{5} + 7 \sqrt{5}$
=$8 \sqrt{5} - 3 \sqrt{5} + 7 \sqrt{5}$
=$15 \sqrt{5} - 3 \sqrt{5}$
=12sqrt5 )