Simplify the Radical Expression 3 square root of 49x^9y^16

$3 \sqrt{49 x^{9} y^{16}}$

Step 1

Rewrite $49 x^{9} y^{16}$ as ${(7 x^{4} y^{8})}^{2} x$ .

Rewrite $49$ as $7^{2}$ .

$3 \sqrt{7^{2} x^{9} y^{16}}$

Factor out $x^{8}$ .

$3 \sqrt{7^{2} (x^{8} x) y^{16}}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$3 \sqrt{7^{2} ({(x^{4})}^{2} x) y^{16}}$

Rewrite $y^{16}$ as ${(y^{8})}^{2}$ .

$3 \sqrt{7^{2} ({(x^{4})}^{2} x) {(y^{8})}^{2}}$

Move $x$ .

$3 \sqrt{7^{2} ({(x^{4})}^{2}) {(y^{8})}^{2} x}$

Rewrite $7^{2} ({(x^{4})}^{2}) {(y^{8})}^{2}$ as ${(7 x^{4} y^{8})}^{2}$ .

$3 \sqrt{{(7 x^{4} y^{8})}^{2} x}$

Step 2

Pull terms out from under the radical.

$3 (| 7 x^{4} y^{8} | \sqrt{x})$

Step 3

Remove non-negative terms from the absolute value.

$3 (7 x^{4} y^{8} \sqrt{x})$

Step 4

Multiply $7$ by $3$ .

$21 x^{4} y^{8} \sqrt{x}$