Simplify ( square root of 9x^3y^2)/( square root of 3)

$\frac{\sqrt{9 x^{3} y^{2}}}{\sqrt{3}}$

Combine $\sqrt{9 x^{3} y^{2}}$ and $\sqrt{3}$ into a single radical.

$\sqrt{\frac{9 x^{3} y^{2}}{3}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{9 x^{3} y^{2}}{3}$ by cancelling the common factors.

Factor $3$ out of $9 x^{3} y^{2}$ .

$\sqrt{\frac{3 (3 x^{3} y^{2})}{3}}$

Factor $3$ out of $3$ .

$\sqrt{\frac{3 (3 x^{3} y^{2})}{3 (1)}}$

Cancel the common factor.

$\sqrt{\frac{3 (3 x^{3} y^{2})}{3 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{3 x^{3} y^{2}}{1}}$

Divide $3 x^{3} y^{2}$ by $1$ .

$\sqrt{3 x^{3} y^{2}}$

Rewrite $3 x^{3} y^{2}$ as ${(x y)}^{2} \cdot (3 x)$ .

Factor out $x^{2}$ .

$\sqrt{3 (x^{2} x) y^{2}}$

Move $x$ .

$\sqrt{3 (x^{2}) y^{2} x}$

Move $3$ .

$\sqrt{(x^{2}) y^{2} \cdot 3 x}$

Rewrite $(x^{2}) y^{2}$ as ${(x y)}^{2}$ .

$\sqrt{{(x y)}^{2} \cdot 3 x}$

Add parentheses.

$\sqrt{{(x y)}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$x y \sqrt{3 x}$