Simplify - square root of 396x^6y^15

$- \sqrt{396 x^{6} y^{15}}$

Step 1

Rewrite $396 x^{6} y^{15}$ as ${(6 x^{3} y^{7})}^{2} \cdot (11 y)$ .

Factor $36$ out of $396$ .

$- \sqrt{36 (11) x^{6} y^{15}}$

Rewrite $36$ as $6^{2}$ .

$- \sqrt{6^{2} \cdot 11 x^{6} y^{15}}$

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

$- \sqrt{6^{2} \cdot 11 {(x^{3})}^{2} y^{15}}$

Factor out $y^{14}$ .

$- \sqrt{6^{2} \cdot 11 {(x^{3})}^{2} (y^{14} y)}$

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

$- \sqrt{6^{2} \cdot 11 {(x^{3})}^{2} ({(y^{7})}^{2} y)}$

Move $11$ .

$- \sqrt{6^{2} {(x^{3})}^{2} {(y^{7})}^{2} \cdot 11 y}$

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

$- \sqrt{{(6 x^{3} y^{7})}^{2} \cdot 11 y}$

Add parentheses.

$- \sqrt{{(6 x^{3} y^{7})}^{2} \cdot (11 y)}$

Step 2

Pull terms out from under the radical.

$- (6 x^{3} y^{7} \sqrt{11 y})$

Step 3

Multiply $6$ by $- 1$ .

$- 6 x^{3} y^{7} \sqrt{11 y}$