Simplifying this radical expression.

Question

As homework I was asked to simply the following radical expression.

$\sqrt{3ax^2+18ax+27a}$

Is following the farthest I can simplify the above expression ?

$\sqrt{3a(x^2+6x+9)}$

Answer 1

$$x^2 + 6x + 9 = (x+3)^2{}{}{}{}{}{}$$

That gives you $$\sqrt{3a(x^2+6x+9)} = \sqrt{3a(x+3)^2} = |x+3|\sqrt{3a}$$