# How do you simplify sqrt12+sqrt27-sqrt3?

Apr 14, 2017

$4 \sqrt{3}$

#### Explanation:

$\sqrt{12} + \sqrt{27} - \sqrt{3}$

By $12 = 2 \cdot 2 \cdot 3$ and $27 = 3 \cdot 3 \cdot 3$,

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

By grouping pairs of the same factors,

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

By simplifying the square-roots of squares,

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

By factoring out $\sqrt{3}$,

$= \left(2 + 3 - 1\right) \sqrt{3} = 4 \sqrt{3}$

I hope that this was clear.