Evaluate ( square root of -24)/( square root of -8)

$\frac{\sqrt{- 24}}{\sqrt{- 8}}$

Step 1

Pull out imaginary unit $i$ .

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

$\frac{\sqrt{- 1 (24)}}{\sqrt{- 8}}$

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

$\frac{\sqrt{- 1} \cdot \sqrt{24}}{\sqrt{- 8}}$

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

$\frac{i \cdot \sqrt{24}}{\sqrt{- 8}}$

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

$\frac{i \cdot \sqrt{24}}{\sqrt{- 1 (8)}}$

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

$\frac{i \cdot \sqrt{24}}{\sqrt{- 1} \cdot \sqrt{8}}$

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

$\frac{i \cdot \sqrt{24}}{i \cdot \sqrt{8}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{24}}{i \cdot \sqrt{8}}$

Rewrite the expression.

$\frac{\sqrt{24}}{\sqrt{8}}$

Step 3

Combine $\sqrt{24}$ and $\sqrt{8}$ into a single radical.

$\sqrt{\frac{24}{8}}$

Step 4

Divide $24$ by $8$ .

$\sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$