Simplify ( square root of 324xy)/(3 square root of 3)

$\frac{\sqrt{324 x y}}{3 \sqrt{3}}$

Step 1

Combine $\sqrt{324 x y}$ and $\sqrt{3}$ into a single radical.

$\frac{\sqrt{\frac{324 x y}{3}}}{3}$

Step 2

Cancel the common factor of $324$ and $3$ .

Factor $3$ out of $324 x y$ .

$\frac{\sqrt{\frac{3 (108 x y)}{3}}}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{\sqrt{\frac{3 (108 x y)}{3 (1)}}}{3}$

Cancel the common factor.

$\frac{\sqrt{\frac{3 (108 x y)}{3 \cdot 1}}}{3}$

Rewrite the expression.

$\frac{\sqrt{\frac{108 x y}{1}}}{3}$

Divide $108 x y$ by $1$ .

$\frac{\sqrt{108 x y}}{3}$

$\frac{\sqrt{108 x y}}{3}$

$\frac{\sqrt{108 x y}}{3}$

Step 3

Simplify the numerator.

Rewrite $108 x y$ as $6^{2} \cdot (3 x y)$ .

Factor $36$ out of $108$ .

$\frac{\sqrt{36 (3) x y}}{3}$

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{6^{2} \cdot 3 x y}}{3}$

Add parentheses.

$\frac{\sqrt{6^{2} \cdot 3 (x y)}}{3}$

Add parentheses.

$\frac{\sqrt{6^{2} \cdot (3 x y)}}{3}$

$\frac{\sqrt{6^{2} \cdot (3 x y)}}{3}$

Pull terms out from under the radical.

$\frac{6 \sqrt{3 x y}}{3}$

$\frac{6 \sqrt{3 x y}}{3}$

Step 4

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \sqrt{3 x y}$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 \sqrt{3 x y}$ by $1$ .

$2 \sqrt{3 x y}$

$2 \sqrt{3 x y}$

$2 \sqrt{3 x y}$

Related Questions