Evaluate ( square root of -192)/( square root of -64)

$\frac{\sqrt{- 192}}{\sqrt{- 64}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 192$ as $- 1 (192)$ .

$\frac{\sqrt{- 1 (192)}}{\sqrt{- 64}}$

Rewrite $\sqrt{- 1 (192)}$ as $\sqrt{- 1} \cdot \sqrt{192}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{192}}{\sqrt{- 64}}$

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

$\frac{i \cdot \sqrt{192}}{\sqrt{- 64}}$

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

$\frac{i \cdot \sqrt{192}}{\sqrt{- 1 (64)}}$

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

$\frac{i \cdot \sqrt{192}}{\sqrt{- 1} \cdot \sqrt{64}}$

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

$\frac{i \cdot \sqrt{192}}{i \cdot \sqrt{64}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{192}}{i \cdot \sqrt{64}}$

Rewrite the expression.

$\frac{\sqrt{192}}{\sqrt{64}}$

Step 3

Combine $\sqrt{192}$ and $\sqrt{64}$ into a single radical.

$\sqrt{\frac{192}{64}}$

Step 4

Divide $192$ by $64$ .

$\sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$