Simplify 4a square root of (16x+16y)/36

$4 a \sqrt{\frac{16 x + 16 y}{36}}$

Step 1

Factor $16$ out of $16 x + 16 y$ .

Factor $16$ out of $16 x$ .

$4 a \sqrt{\frac{16 (x) + 16 y}{36}}$

Factor $16$ out of $16 y$ .

$4 a \sqrt{\frac{16 (x) + 16 (y)}{36}}$

Factor $16$ out of $16 (x) + 16 (y)$ .

$4 a \sqrt{\frac{16 (x + y)}{36}}$

Step 2

Reduce the expression $\frac{16 (x + y)}{36}$ by cancelling the common factors.

Factor $4$ out of $16 (x + y)$ .

$4 a \sqrt{\frac{4 (4 (x + y))}{36}}$

Factor $4$ out of $36$ .

$4 a \sqrt{\frac{4 (4 (x + y))}{4 (9)}}$

Cancel the common factor.

$4 a \sqrt{\frac{4 (4 (x + y))}{4 \cdot 9}}$

Rewrite the expression.

$4 a \sqrt{\frac{4 (x + y)}{9}}$

Step 3

Rewrite $\frac{4 (x + y)}{9}$ as ${(\frac{2}{3})}^{2} (x + y)$ .

Factor the perfect power $2^{2}$ out of $4 (x + y)$ .

$4 a \sqrt{\frac{2^{2} (x + y)}{9}}$

Factor the perfect power $3^{2}$ out of $9$ .

$4 a \sqrt{\frac{2^{2} (x + y)}{3^{2} \cdot 1}}$

Rearrange the fraction $\frac{2^{2} (x + y)}{3^{2} \cdot 1}$ .

$4 a \sqrt{{(\frac{2}{3})}^{2} (x + y)}$

Step 4

Pull terms out from under the radical.

$4 a (\frac{2}{3} \sqrt{x + y})$

Step 5

Combine $\frac{2}{3}$ and $\sqrt{x + y}$ .

$4 a \frac{2 \sqrt{x + y}}{3}$

Step 6

Multiply $4 a \frac{2 \sqrt{x + y}}{3}$ .

Combine $4$ and $\frac{2 \sqrt{x + y}}{3}$ .

$a \frac{4 (2 \sqrt{x + y})}{3}$

Multiply $2$ by $4$ .

$a \frac{8 \sqrt{x + y}}{3}$

Combine $a$ and $\frac{8 \sqrt{x + y}}{3}$ .

$\frac{a (8 \sqrt{x + y})}{3}$

Step 7

Move $8$ to the left of $a$ .

$\frac{8 a \sqrt{x + y}}{3}$