Algebra Examples

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

Step 1

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

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

Step 2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

Factor $3$ out of $3$ .

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

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

Step 2.2

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

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

Step 3

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

Tap for more steps...

Step 3.1

Factor out $x^{2}$ .

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

Step 3.2

Move $x$ .

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

Step 3.3

Move $3$ .

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

Step 3.4

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

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

Step 3.5

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$x y \sqrt{3 x}$