Trigonometry Examples

$\sqrt{{(\sqrt{3} - 0)}^{2} (- \sqrt{5} - 0^{2})}$

Step 1

Multiply $- 1$ by $0$ .

$\sqrt{{(\sqrt{3} + 0)}^{2} (- \sqrt{5} - 0^{2})}$

Step 2

Add $\sqrt{3}$ and $0$ .

$\sqrt{{\sqrt{3}}^{2} (- \sqrt{5} - 0^{2})}$

Step 3

Raising $0$ to any positive power yields $0$ .

$\sqrt{{\sqrt{3}}^{2} (- \sqrt{5} - 0)}$

Step 4

Multiply $- 1$ by $0$ .

$\sqrt{{\sqrt{3}}^{2} (- \sqrt{5} + 0)}$

Step 5

Add $- \sqrt{5}$ and $0$ .

$\sqrt{{\sqrt{3}}^{2} \cdot - 1 \sqrt{5}}$

Step 6

Factor out negative.

$\sqrt{- ({\sqrt{3}}^{2} \sqrt{5})}$

Step 7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\sqrt{- ({(3^{\frac{1}{2}})}^{2} \sqrt{5})}$

Step 7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{- (3^{\frac{1}{2} \cdot 2} \sqrt{5})}$

Step 7.3

Combine $\frac{1}{2}$ and $2$ .

$\sqrt{- (3^{\frac{2}{2}} \sqrt{5})}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$\sqrt{- (3^{\frac{2}{2}} \sqrt{5})}$

Step 7.4.2

Rewrite the expression.

$\sqrt{- (3^{1} \sqrt{5})}$

Step 7.5

Evaluate the exponent.

$\sqrt{- (3 \sqrt{5})}$

$\sqrt{- 1 \cdot 3 \sqrt{5}}$

Step 8

Multiply $- 1$ by $3$ .

$\sqrt{- 3 \sqrt{5}}$

Step 9

Rewrite $- 3 \sqrt{5}$ as $i^{2} \cdot (3 \sqrt{5})$ .

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Step 9.1

Rewrite $- 3$ as $- 1 (3)$ .

$\sqrt{- 1 (3) \sqrt{5}}$

Step 9.2

Rewrite $- 1$ as $i^{2}$ .

$\sqrt{i^{2} \cdot 3 \sqrt{5}}$

Step 9.3

Add parentheses.

$\sqrt{i^{2} \cdot (3 \sqrt{5})}$

Step 10

Pull terms out from under the radical.

$i \sqrt{3 \sqrt{5}}$