Simplify ( square root of 144xy)/(2 square root of 2)

$\frac{\sqrt{144 x y}}{2 \sqrt{2}}$

Step 1

Combine $\sqrt{144 x y}$ and $\sqrt{2}$ into a single radical.

$\frac{\sqrt{\frac{144 x y}{2}}}{2}$

Step 2

Cancel the common factor of $144$ and $2$ .

Factor $2$ out of $144 x y$ .

$\frac{\sqrt{\frac{2 (72 x y)}{2}}}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{\sqrt{\frac{2 (72 x y)}{2 (1)}}}{2}$

Cancel the common factor.

$\frac{\sqrt{\frac{2 (72 x y)}{2 \cdot 1}}}{2}$

Rewrite the expression.

$\frac{\sqrt{\frac{72 x y}{1}}}{2}$

Divide $72 x y$ by $1$ .

$\frac{\sqrt{72 x y}}{2}$

$\frac{\sqrt{72 x y}}{2}$

$\frac{\sqrt{72 x y}}{2}$

Step 3

Simplify the numerator.

Rewrite $72 x y$ as $6^{2} \cdot (2 x y)$ .

Factor $36$ out of $72$ .

$\frac{\sqrt{36 (2) x y}}{2}$

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

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

Add parentheses.

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

Add parentheses.

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

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

Pull terms out from under the radical.

$\frac{6 \sqrt{2 x y}}{2}$

$\frac{6 \sqrt{2 x y}}{2}$

Step 4

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \sqrt{2 x y}$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$3 \sqrt{2 x y}$

$3 \sqrt{2 x y}$

$3 \sqrt{2 x y}$

Related Questions