Simplify the Radical Expression x^2y^2 square root of 28x^6y^6

$x^{2} y^{2} \sqrt{28 x^{6} y^{6}}$

Step 1

Rewrite $28 x^{6} y^{6}$ as ${(2 x^{3} y^{3})}^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$x^{2} y^{2} \sqrt{4 (7) x^{6} y^{6}}$

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

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

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

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

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

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

Move $7$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Remove non-negative terms from the absolute value.

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