Evaluate ( square root of -24)/( square root of -2)

$\frac{\sqrt{- 24}}{\sqrt{- 2}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 24$ as $- 1 (24)$ .

$\frac{\sqrt{- 1 (24)}}{\sqrt{- 2}}$

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{24}}{\sqrt{- 2}}$

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

$\frac{i \cdot \sqrt{24}}{\sqrt{- 2}}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{i \cdot \sqrt{24}}{\sqrt{- 1 (2)}}$

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

$\frac{i \cdot \sqrt{24}}{\sqrt{- 1} \cdot \sqrt{2}}$

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

$\frac{i \cdot \sqrt{24}}{i \cdot \sqrt{2}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{24}}{i \cdot \sqrt{2}}$

Rewrite the expression.

$\frac{\sqrt{24}}{\sqrt{2}}$

Step 3

Combine $\sqrt{24}$ and $\sqrt{2}$ into a single radical.

$\sqrt{\frac{24}{2}}$

Step 4

Divide $24$ by $2$ .

$\sqrt{12}$

Step 5

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3)}$

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

$\sqrt{2^{2} \cdot 3}$

Step 6

Pull terms out from under the radical.

$2 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$