Trigonometry Examples

$\sqrt{64 x^{5} y^{13}}$

Step 1

Rewrite $64 x^{5} y^{13}$ as ${(8 x^{2} y^{6})}^{2} (x y)$ .

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Step 1.1

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

$\sqrt{8^{2} x^{5} y^{13}}$

Step 1.2

Factor out $x^{4}$ .

$\sqrt{8^{2} (x^{4} x) y^{13}}$

Step 1.3

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

$\sqrt{8^{2} ({(x^{2})}^{2} x) y^{13}}$

Step 1.4

Factor out $y^{12}$ .

$\sqrt{8^{2} ({(x^{2})}^{2} x) (y^{12} y)}$

Step 1.5

Rewrite $y^{12}$ as ${(y^{6})}^{2}$ .

$\sqrt{8^{2} ({(x^{2})}^{2} x) ({(y^{6})}^{2} y)}$

Step 1.6

Move $x$ .

$\sqrt{8^{2} ({(x^{2})}^{2}) {(y^{6})}^{2} x y}$

Step 1.7

Rewrite $8^{2} ({(x^{2})}^{2}) {(y^{6})}^{2}$ as ${(8 x^{2} y^{6})}^{2}$ .

$\sqrt{{(8 x^{2} y^{6})}^{2} x y}$

Step 1.8

Add parentheses.

$\sqrt{{(8 x^{2} y^{6})}^{2} (x y)}$

Step 2

Pull terms out from under the radical.

$8 x^{2} y^{6} \sqrt{x y}$