Simplify the Radical Expression square root of 16xy

$\sqrt{16 x y}$

Step 1

Rewrite $16 x y$ as ${(2^{2})}^{2} (x y)$ .

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} x y}$

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$| 2^{2} | \sqrt{x y}$

Step 3

Raise $2$ to the power of $2$ .

$| 4 | \sqrt{x y}$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$4 \sqrt{x y}$