# How do you add sqrt24 + sqrt54?

Apr 4, 2015

The answer is $5 \sqrt{6}$

In this type of problems, there is a rule zero: Prime Factorization.

$24 = {2}^{3} \cdot 3$ and $54 = {3}^{3} \cdot 2$

So

$\sqrt{24} + \sqrt{54} = \sqrt{{2}^{3} \cdot 3} + \sqrt{{3}^{3} \cdot 2}$

$= \sqrt{{2}^{2} \cdot 2 \cdot 3} + \sqrt{{3}^{2} \cdot 3 \cdot 2}$

$= 2 \sqrt{2 \cdot 3} + 3 \sqrt{3 \cdot 2}$

$2 \sqrt{6} + 3 \sqrt{6} = \sqrt{6} \left(2 + 3\right) = 5 \sqrt{6}$