Simplify square root of 24x^2y^6

$\sqrt{24 x^{2} y^{6}}$

Step 1

Rewrite $24 x^{2} y^{6}$ as ${(2 x y^{3})}^{2} \cdot 6$ .

Factor $4$ out of $24$ .

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

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

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

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

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

Move $6$ .

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

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

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

Step 2

Pull terms out from under the radical.

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