Simplify ( square root of 400xy)/(2 square root of 2)

$\frac{\sqrt{400 x y}}{2 \sqrt{2}}$

Step 1

Combine $\sqrt{400 x y}$ and $\sqrt{2}$ into a single radical.

$\frac{\sqrt{\frac{400 x y}{2}}}{2}$

Step 2

Cancel the common factor of $400$ and $2$ .

Factor $2$ out of $400 x y$ .

$\frac{\sqrt{\frac{2 (200 x y)}{2}}}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{\sqrt{\frac{2 (200 x y)}{2 (1)}}}{2}$

Cancel the common factor.

$\frac{\sqrt{\frac{2 (200 x y)}{2 \cdot 1}}}{2}$

Rewrite the expression.

$\frac{\sqrt{\frac{200 x y}{1}}}{2}$

Divide $200 x y$ by $1$ .

$\frac{\sqrt{200 x y}}{2}$

$\frac{\sqrt{200 x y}}{2}$

$\frac{\sqrt{200 x y}}{2}$

Step 3

Simplify the numerator.

Rewrite $200 x y$ as $10^{2} \cdot (2 x y)$ .

Factor $100$ out of $200$ .

$\frac{\sqrt{100 (2) x y}}{2}$

Rewrite $100$ as $10^{2}$ .

$\frac{\sqrt{10^{2} \cdot 2 x y}}{2}$

Add parentheses.

$\frac{\sqrt{10^{2} \cdot 2 (x y)}}{2}$

Add parentheses.

$\frac{\sqrt{10^{2} \cdot (2 x y)}}{2}$

$\frac{\sqrt{10^{2} \cdot (2 x y)}}{2}$

Pull terms out from under the radical.

$\frac{10 \sqrt{2 x y}}{2}$

$\frac{10 \sqrt{2 x y}}{2}$

Step 4

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 \sqrt{2 x y}$ .

$\frac{2 (5 \sqrt{2 x y})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (5 \sqrt{2 x y})}{2 (1)}$

Cancel the common factor.

$\frac{2 (5 \sqrt{2 x y})}{2 \cdot 1}$

Rewrite the expression.

$\frac{5 \sqrt{2 x y}}{1}$

Divide $5 \sqrt{2 x y}$ by $1$ .

$5 \sqrt{2 x y}$

$5 \sqrt{2 x y}$

$5 \sqrt{2 x y}$

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