Basic Math Examples

$\frac{\sqrt{- 8}}{- 2}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

$\frac{\sqrt{- 1} \cdot \sqrt{8}}{- 2}$

Step 1.3

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

$\frac{i \cdot \sqrt{8}}{- 2}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Factor $4$ out of $8$ .

$\frac{i \sqrt{4 (2)}}{- 2}$

Step 2.1.2

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

$\frac{i \sqrt{2^{2} \cdot 2}}{- 2}$

Step 2.2

Pull terms out from under the radical.

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

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Cancel the common factor of $2$ and $- 2$ .

Tap for more steps...

Step 3.2.1

Factor $2$ out of $2 i \sqrt{2}$ .

$\frac{2 (i \sqrt{2})}{- 2}$

Step 3.2.2

Move the negative one from the denominator of $\frac{i \sqrt{2}}{- 1}$ .

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

Step 3.3

Rewrite $- 1 \cdot (i \sqrt{2})$ as $- (i \sqrt{2})$ .

$- i \sqrt{2}$