How do you simplify 2sqrt20 + 8sqrt45 - sqrt80?

Jun 9, 2016

You first factorise everthing under the root, trying to find squares:

Explanation:

$20 = 4 \times 5 = {2}^{2} \times 5$
$45 = 9 \times 5 = {3}^{2} \times 5$
$80 = 16 \times 5 = {4}^{2} \times 5$

We can take the squares out from underneath the roots
$\sqrt{20} = 2 \sqrt{5}$
$\sqrt{45} = 3 \sqrt{5}$
$\sqrt{80} = 4 \sqrt{5}$

We may add roots with the same argument:

$2 \sqrt{5} + 3 \sqrt{5} + 4 \sqrt{5} = \left(2 + 3 + 4\right) \sqrt{5} = 9 \sqrt{5}$