Trigonometry Examples

$\frac{\sqrt{- 64}}{\sqrt{2}}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 64$ as $- 1 (64)$ .

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

Step 1.2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{64}}{\sqrt{2}}$

Step 1.3

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

$\frac{i \cdot \sqrt{64}}{\sqrt{2}}$

Step 2

Combine $\sqrt{64}$ and $\sqrt{2}$ into a single radical.

$i \cdot \sqrt{\frac{64}{2}}$

Step 3

Divide $64$ by $2$ .

$i \cdot \sqrt{32}$

Step 4

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

Tap for more steps...

Step 4.1

Factor $16$ out of $32$ .

$i \cdot \sqrt{16 (2)}$

Step 4.2

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

$i \cdot \sqrt{4^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$i \cdot (4 \sqrt{2})$

Step 6

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

$4 i \sqrt{2}$