Simplify ( square root of 2025xy)/(3 square root of 3)

$\frac{\sqrt{2025 x y}}{3 \sqrt{3}}$

Step 1

Combine $\sqrt{2025 x y}$ and $\sqrt{3}$ into a single radical.

$\frac{\sqrt{\frac{2025 x y}{3}}}{3}$

Step 2

Cancel the common factor of $2025$ and $3$ .

Factor $3$ out of $2025 x y$ .

$\frac{\sqrt{\frac{3 (675 x y)}{3}}}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{\sqrt{\frac{3 (675 x y)}{3 (1)}}}{3}$

Cancel the common factor.

$\frac{\sqrt{\frac{3 (675 x y)}{3 \cdot 1}}}{3}$

Rewrite the expression.

$\frac{\sqrt{\frac{675 x y}{1}}}{3}$

Divide $675 x y$ by $1$ .

$\frac{\sqrt{675 x y}}{3}$

$\frac{\sqrt{675 x y}}{3}$

$\frac{\sqrt{675 x y}}{3}$

Step 3

Simplify the numerator.

Rewrite $675 x y$ as $15^{2} \cdot (3 x y)$ .

Factor $225$ out of $675$ .

$\frac{\sqrt{225 (3) x y}}{3}$

Rewrite $225$ as $15^{2}$ .

$\frac{\sqrt{15^{2} \cdot 3 x y}}{3}$

Add parentheses.

$\frac{\sqrt{15^{2} \cdot 3 (x y)}}{3}$

Add parentheses.

$\frac{\sqrt{15^{2} \cdot (3 x y)}}{3}$

$\frac{\sqrt{15^{2} \cdot (3 x y)}}{3}$

Pull terms out from under the radical.

$\frac{15 \sqrt{3 x y}}{3}$

$\frac{15 \sqrt{3 x y}}{3}$

Step 4

Cancel the common factor of $15$ and $3$ .

Factor $3$ out of $15 \sqrt{3 x y}$ .

$\frac{3 (5 \sqrt{3 x y})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (5 \sqrt{3 x y})}{3 (1)}$

Cancel the common factor.

$\frac{3 (5 \sqrt{3 x y})}{3 \cdot 1}$

Rewrite the expression.

$\frac{5 \sqrt{3 x y}}{1}$

Divide $5 \sqrt{3 x y}$ by $1$ .

$5 \sqrt{3 x y}$

$5 \sqrt{3 x y}$

$5 \sqrt{3 x y}$

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