Simplify square root of 80x^8y^4

$\sqrt{80 x^{8} y^{4}}$

Step 1

Rewrite $80 x^{8} y^{4}$ as ${(4 x^{4} y^{2})}^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x^{8} y^{4}}$

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

$\sqrt{4^{2} \cdot 5 x^{8} y^{4}}$

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

$\sqrt{4^{2} \cdot 5 {(x^{4})}^{2} y^{4}}$

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

$\sqrt{4^{2} \cdot 5 {(x^{4})}^{2} {(y^{2})}^{2}}$

Move $5$ .

$\sqrt{4^{2} {(x^{4})}^{2} {(y^{2})}^{2} \cdot 5}$

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

$\sqrt{{(4 x^{4} y^{2})}^{2} \cdot 5}$

Step 2

Pull terms out from under the radical.

$4 x^{4} y^{2} \sqrt{5}$