Simplify the Radical Expression x^2y^2 square root of 63x^2y^6

$x^{2} y^{2} \sqrt{63 x^{2} y^{6}}$

Step 1

Rewrite $63 x^{2} y^{6}$ as ${(3 x y^{3})}^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$x^{2} y^{2} \sqrt{9 (7) x^{2} y^{6}}$

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

$x^{2} y^{2} \sqrt{3^{2} \cdot 7 x^{2} y^{6}}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Move $7$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{7} x^{2} y^{2} | 3 x y^{3} |$

Step 4

Remove non-negative terms from the absolute value.

$\sqrt{7} x^{2} y^{2} \cdot 3 | x y^{3} |$