Trigonometry Examples

$2 \sqrt{- 50} - 3 \sqrt{- 8}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

$- 50$ as

$- 1 (50)$ .

$2 \sqrt{- 1 (50)} - 3 \sqrt{- 8}$

Step 1.2

Rewrite

$\sqrt{- 1 (50)}$ as

$\sqrt{- 1} \cdot \sqrt{50}$ .

$2 (\sqrt{- 1} \cdot \sqrt{50}) - 3 \sqrt{- 8}$

Step 1.3

Rewrite

$\sqrt{- 1}$ as

$i$ .

$2 (i \cdot \sqrt{50}) - 3 \sqrt{- 8}$

Step 1.4

Rewrite

$50$ as

$5^{2} \cdot 2$ .

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Step 1.4.1

Factor

$25$ out of

$50$ .

$2 (i \cdot \sqrt{25 (2)}) - 3 \sqrt{- 8}$

Step 1.4.2

Rewrite

$25$ as

$5^{2}$ .

$2 (i \cdot \sqrt{5^{2} \cdot 2}) - 3 \sqrt{- 8}$

$2 (i \cdot \sqrt{5^{2} \cdot 2}) - 3 \sqrt{- 8}$

Step 1.5

Pull terms out from under the radical.

$2 (i \cdot (5 \sqrt{2})) - 3 \sqrt{- 8}$

Step 1.6

Move

$5$ to the left of

$i$ .

$2 (5 \cdot i \sqrt{2}) - 3 \sqrt{- 8}$

Step 1.7

Multiply

$5$ by

$2$ .

$10 (i \sqrt{2}) - 3 \sqrt{- 8}$

Step 1.8

Rewrite

$- 8$ as

$- 1 (8)$ .

$10 i \sqrt{2} - 3 \sqrt{- 1 (8)}$

Step 1.9

Rewrite

$\sqrt{- 1 (8)}$ as

$\sqrt{- 1} \cdot \sqrt{8}$ .

$10 i \sqrt{2} - 3 (\sqrt{- 1} \cdot \sqrt{8})$

Step 1.10

Rewrite

$\sqrt{- 1}$ as

$i$ .

$10 i \sqrt{2} - 3 (i \cdot \sqrt{8})$

Step 1.11

Rewrite

$8$ as

$2^{2} \cdot 2$ .

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Step 1.11.1

Factor

$4$ out of

$8$ .

$10 i \sqrt{2} - 3 (i \cdot \sqrt{4 (2)})$

Step 1.11.2

Rewrite

$4$ as

$2^{2}$ .

$10 i \sqrt{2} - 3 (i \cdot \sqrt{2^{2} \cdot 2})$

$10 i \sqrt{2} - 3 (i \cdot \sqrt{2^{2} \cdot 2})$

Step 1.12

Pull terms out from under the radical.

$10 i \sqrt{2} - 3 (i \cdot (2 \sqrt{2}))$

Step 1.13

Move

$2$ to the left of

$i$ .

$10 i \sqrt{2} - 3 (2 \cdot i \sqrt{2})$

Step 1.14

Multiply

$2$ by

$- 3$ .

$10 i \sqrt{2} - 6 i \sqrt{2}$

$10 i \sqrt{2} - 6 i \sqrt{2}$

Step 2

Subtract

$6 i \sqrt{2}$ from

$10 i \sqrt{2}$ .

$4 i \sqrt{2}$

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