Trigonometry Examples

$\sqrt{500 x^{102} y^{30}}$

Step 1

Rewrite $500 x^{102} y^{30}$ as ${(10 x^{51} y^{15})}^{2} \cdot 5$ .

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Factor $100$ out of $500$ .

$\sqrt{100 (5) x^{102} y^{30}}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 5 x^{102} y^{30}}$

Rewrite $x^{102}$ as ${(x^{51})}^{2}$ .

$\sqrt{10^{2} \cdot 5 {(x^{51})}^{2} y^{30}}$

Rewrite $y^{30}$ as ${(y^{15})}^{2}$ .

$\sqrt{10^{2} \cdot 5 {(x^{51})}^{2} {(y^{15})}^{2}}$

Move $5$ .

$\sqrt{10^{2} {(x^{51})}^{2} {(y^{15})}^{2} \cdot 5}$

Rewrite $10^{2} {(x^{51})}^{2} {(y^{15})}^{2}$ as ${(10 x^{51} y^{15})}^{2}$ .

$\sqrt{{(10 x^{51} y^{15})}^{2} \cdot 5}$

Step 2

Pull terms out from under the radical.

$10 x^{51} y^{15} \sqrt{5}$