Trigonometry Examples

$\sqrt{- 500}$

Step 1

Rewrite $- 500$ as $- 1 (500)$ .

$\sqrt{- 1 (500)}$

Step 2

Rewrite $\sqrt{- 1 (500)}$ as $\sqrt{- 1} \cdot \sqrt{500}$ .

$\sqrt{- 1} \cdot \sqrt{500}$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{500}$

Step 4

Rewrite $500$ as $10^{2} \cdot 5$ .

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Step 4.1

Factor $100$ out of $500$ .

$i \cdot \sqrt{100 (5)}$

Step 4.2

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

$i \cdot \sqrt{10^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$i \cdot (10 \sqrt{5})$

Step 6

Move $10$ to the left of $i$ .

$10 i \sqrt{5}$