Trigonometry Examples

$2 \sqrt{- 32} - 5 \sqrt{- 8}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 32$ as $- 1 (32)$ .

$2 \sqrt{- 1 (32)} - 5 \sqrt{- 8}$

Step 1.2

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$2 (\sqrt{- 1} \cdot \sqrt{32}) - 5 \sqrt{- 8}$

Step 1.3

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

$2 (i \cdot \sqrt{32}) - 5 \sqrt{- 8}$

Step 1.4

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.4.1

Factor $16$ out of $32$ .

$2 (i \cdot \sqrt{16 (2)}) - 5 \sqrt{- 8}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$2 (i \cdot \sqrt{4^{2} \cdot 2}) - 5 \sqrt{- 8}$

$2 (i \cdot \sqrt{4^{2} \cdot 2}) - 5 \sqrt{- 8}$

Step 1.5

Pull terms out from under the radical.

$2 (i \cdot (4 \sqrt{2})) - 5 \sqrt{- 8}$

Step 1.6

Move $4$ to the left of $i$ .

$2 (4 \cdot i \sqrt{2}) - 5 \sqrt{- 8}$

Step 1.7

Multiply $4$ by $2$ .

$8 (i \sqrt{2}) - 5 \sqrt{- 8}$

Step 1.8

Rewrite $- 8$ as $- 1 (8)$ .

$8 i \sqrt{2} - 5 \sqrt{- 1 (8)}$

Step 1.9

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$8 i \sqrt{2} - 5 (\sqrt{- 1} \cdot \sqrt{8})$

Step 1.10

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

$8 i \sqrt{2} - 5 (i \cdot \sqrt{8})$

Step 1.11

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.11.1

Factor $4$ out of $8$ .

$8 i \sqrt{2} - 5 (i \cdot \sqrt{4 (2)})$

Step 1.11.2

Rewrite $4$ as $2^{2}$ .

$8 i \sqrt{2} - 5 (i \cdot \sqrt{2^{2} \cdot 2})$

$8 i \sqrt{2} - 5 (i \cdot \sqrt{2^{2} \cdot 2})$

Step 1.12

Pull terms out from under the radical.

$8 i \sqrt{2} - 5 (i \cdot (2 \sqrt{2}))$

Step 1.13

Move $2$ to the left of $i$ .

$8 i \sqrt{2} - 5 (2 \cdot i \sqrt{2})$

Step 1.14

Multiply $2$ by $- 5$ .

$8 i \sqrt{2} - 10 i \sqrt{2}$

$8 i \sqrt{2} - 10 i \sqrt{2}$

Step 2

Subtract $10 i \sqrt{2}$ from $8 i \sqrt{2}$ .

$- 2 i \sqrt{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$