Simplify 3 square root of 9(x+y)^5

$3 \sqrt{9 {(x + y)}^{5}}$

Step 1

Rewrite $9 {(x + y)}^{5}$ as ${(3 {(x + y)}^{2})}^{2} (x + y)$ .

Rewrite $9$ as $3^{2}$ .

$3 \sqrt{3^{2} {(x + y)}^{5}}$

Factor out ${(x + y)}^{4}$ .

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

Rewrite ${(x + y)}^{4}$ as ${({(x + y)}^{2})}^{2}$ .

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

Rewrite $3^{2} {({(x + y)}^{2})}^{2}$ as ${(3 {(x + y)}^{2})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $3$ by $3$ .

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