# How do you simplify asqrt27-2sqrt(3a^2)?

Aug 23, 2016

If $a \in \mathbb{R}$ then $a \sqrt{27} - 2 \sqrt{3 {a}^{2}} = \left(3 a - 2 \left\mid a \right\mid\right) \sqrt{3}$

If $a \ge 0$ then $a \sqrt{27} - 2 \sqrt{3 {a}^{2}} = a \sqrt{3}$

#### Explanation:

Assuming $a$ is a Real number:

$a \sqrt{27} - 2 \sqrt{3 {a}^{2}}$

$= a \sqrt{{3}^{2} \cdot 3} - 2 \sqrt{{a}^{2} \cdot 3}$

$= a \sqrt{{3}^{2}} \sqrt{3} - 2 \sqrt{{a}^{2}} \sqrt{3}$

$= \left(3 a - 2 \left\mid a \right\mid\right) \sqrt{3}$

If in addition $a \ge 0$ then $3 a - 2 \left\mid a \right\mid = 3 a - 2 a = a$ and

$a \sqrt{27} - 2 \sqrt{3 {a}^{2}} = a \sqrt{3}$