# How would you simplify sqrt (9x^3)?

Feb 1, 2016

$3 x \sqrt{x}$
We start out with $\sqrt{9 {x}^{3}}$. To solve this we simplify the values into their smallest factors. For $9$, that's pretty easy; the smallest it goes is $3 \cdot 3$ or ${3}^{2}$. ${x}^{3}$ can be simplified to $x \cdot x \cdot x$ or ${x}^{2} \cdot x$.
If we rewrite the expression, it becomes $\sqrt{{3}^{2} \cdot {x}^{2} \cdot x}$. Square root of a square cancels out, like this cancel(sqrt(3^cancel(2).
$\sqrt{{3}^{2}}$ is just $3$. Likewise $\sqrt{{x}^{2}}$ simplifys to $x$. Now the expression is $3 x \sqrt{x}$.