Trigonometry Examples

$- 8 \sqrt{\frac{- 8^{2} - 4 \cdot 16 \cdot 1}{2 (16)}}$

Step 1

Raise $8$ to the power of $2$ .

$- 8 \sqrt{\frac{- 1 \cdot 64 - 4 \cdot 16 \cdot 1}{2 (16)}}$

Step 2

Multiply $- 1$ by $64$ .

$- 8 \sqrt{\frac{- 64 - 4 \cdot 16 \cdot 1}{2 (16)}}$

Step 3

Multiply $- 4 \cdot 16 \cdot 1$ .

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Step 3.1

Multiply $- 4$ by $16$ .

$- 8 \sqrt{\frac{- 64 - 64 \cdot 1}{2 (16)}}$

Step 3.2

Multiply $- 64$ by $1$ .

$- 8 \sqrt{\frac{- 64 - 64}{2 (16)}}$

Step 4

Subtract $64$ from $- 64$ .

$- 8 \sqrt{\frac{- 128}{2 (16)}}$

Step 5

Reduce the expression $\frac{- 128}{2 (16)}$ by cancelling the common factors.

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Step 5.1

Factor $2$ out of $- 128$ .

$- 8 \sqrt{\frac{2 \cdot - 64}{2 \cdot 16}}$

Step 5.2

Factor $2$ out of $2 \cdot 16$ .

$- 8 \sqrt{\frac{2 \cdot - 64}{2 (16)}}$

Step 5.3

Cancel the common factor.

$- 8 \sqrt{\frac{2 \cdot - 64}{2 \cdot 16}}$

Step 5.4

Rewrite the expression.

$- 8 \sqrt{\frac{- 64}{16}}$

Step 6

Divide $- 64$ by $16$ .

$- 8 \sqrt{- 4}$

Step 7

Rewrite $- 4$ as $- 1 (4)$ .

$- 8 \sqrt{- 1 (4)}$

Step 8

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- 8 (\sqrt{- 1} \cdot \sqrt{4})$

Step 9

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

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

Step 10

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

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

Step 11

Pull terms out from under the radical, assuming positive real numbers.

$- 8 (i \cdot 2)$

Step 12

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

$- 8 (2 \cdot i)$

Step 13

Multiply $2$ by $- 8$ .

$- 16 i$