# How do you simplify sqrt 6 + sqrt24?

May 27, 2016

$3 \sqrt{6}$

#### Explanation:

Look at the prime factorisations of $6$ and $24$:

$6 = 2 \times 3$

$24 = 2 \times 2 \times 2 \times 3 = {2}^{2} \cdot 6$

Since $6$ contains no square factors, $\sqrt{6}$ cannot be simplified.

Since $24$ has a square factor ${2}^{2}$, we can simplify $\sqrt{24}$:

$\sqrt{24} = \sqrt{{2}^{2} \cdot 6} = \sqrt{{2}^{2}} \cdot \sqrt{6} = 2 \sqrt{6}$

Then:

$\sqrt{6} + \sqrt{24} = \sqrt{6} + 2 \sqrt{6} = 3 \sqrt{6}$