Simplify square root of 448x^6y^15

$\sqrt{448 x^{6} y^{15}}$

Step 1

Rewrite $448 x^{6} y^{15}$ as ${(8 x^{3} y^{7})}^{2} \cdot (7 y)$ .

Factor $64$ out of $448$ .

$\sqrt{64 (7) x^{6} y^{15}}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 7 x^{6} y^{15}}$

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

$\sqrt{8^{2} \cdot 7 {(x^{3})}^{2} y^{15}}$

Factor out $y^{14}$ .

$\sqrt{8^{2} \cdot 7 {(x^{3})}^{2} (y^{14} y)}$

Rewrite $y^{14}$ as ${(y^{7})}^{2}$ .

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

Move $7$ .

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

Rewrite $8^{2} {(x^{3})}^{2} {(y^{7})}^{2}$ as ${(8 x^{3} y^{7})}^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$8 x^{3} y^{7} \sqrt{7 y}$