Basic Math Examples

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

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Combine $\sqrt{8}$ and $\sqrt{2}$ into a single radical.

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

Step 3

Simplify the expression.

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Step 3.1

Divide $8$ by $2$ .

$i \cdot \sqrt{4}$

Step 3.2

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

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

Step 4

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

$i \cdot 2$

Step 5

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

$2 i$