# How do you simplify sqrt(27x^4 )?

$3 \sqrt{3} {x}^{2}$
First, note that $\sqrt{27 {x}^{4}} = \sqrt{27} \cdot \sqrt{{x}^{4}}$. Next, since $27 = 9 \cdot 3 = {3}^{2} \cdot 3$, we can say $\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \cdot \sqrt{3}$.
Also, $\sqrt{{x}^{4}} = \sqrt{{\left({x}^{2}\right)}^{2}} = {x}^{2}$ (in general, $\sqrt{{y}^{2}} = | y |$, but if $y = {x}^{2}$, then $y \setminus \ge q 0$ anyway so we can get rid of the absolute value sign).