How do you simplify sqrt75+sqrt108?

Oct 6, 2015

In cases like this it often helps to factorize first.

Explanation:

Factorizing means you write a number in the form of a multiplication of smaller numbers (primes).
So you can write:

$75 = 3 \cdot 5 \cdot 5$ and $108 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3$

Now isolate the squares:
$75 = 3 \cdot {5}^{2}$ and $108 = 3 \cdot {2}^{2} \cdot {3}^{2}$

You can simplify by taking the squares from under the root (where they are unsquared of course):

$\sqrt{75} + \sqrt{108} = \sqrt{3 \cdot {5}^{2}} + \sqrt{3 \cdot {2}^{2} \cdot {3}^{3}} =$

$5 \cdot \sqrt{3} + 2 \cdot 3 \cdot \sqrt{3} = 5 \sqrt{3} + 6 \sqrt{3} = 11 \sqrt{3}$