Trigonometry Examples

$3 \sqrt{- 162}$

Step 1

Rewrite $- 162$ as $- 1 (162)$ .

$3 \sqrt{- 1 (162)}$

Step 2

Rewrite $\sqrt{- 1 (162)}$ as $\sqrt{- 1} \cdot \sqrt{162}$ .

$3 (\sqrt{- 1} \cdot \sqrt{162})$

Step 3

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

$3 (i \cdot \sqrt{162})$

Step 4

Rewrite $162$ as $9^{2} \cdot 2$ .

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Step 4.1

Factor $81$ out of $162$ .

$3 (i \cdot \sqrt{81 (2)})$

Step 4.2

Rewrite $81$ as $9^{2}$ .

$3 (i \cdot \sqrt{9^{2} \cdot 2})$

Step 5

Pull terms out from under the radical.

$3 (i \cdot (9 \sqrt{2}))$

Step 6

Simplify the expression.

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Step 6.1

Move $9$ to the left of $i$ .

$3 (9 \cdot i \sqrt{2})$

Step 6.2

Multiply $9$ by $3$ .

$27 i \sqrt{2}$