Evaluate ( square root of -16)/( square root of -8)

$\frac{\sqrt{- 16}}{\sqrt{- 8}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 16$ as $- 1 (16)$ .

$\frac{\sqrt{- 1 (16)}}{\sqrt{- 8}}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{16}}{\sqrt{- 8}}$

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

$\frac{i \cdot \sqrt{16}}{\sqrt{- 8}}$

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

$\frac{i \cdot \sqrt{16}}{\sqrt{- 1 (8)}}$

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

$\frac{i \cdot \sqrt{16}}{\sqrt{- 1} \cdot \sqrt{8}}$

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

$\frac{i \cdot \sqrt{16}}{i \cdot \sqrt{8}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{16}}{i \cdot \sqrt{8}}$

Rewrite the expression.

$\frac{\sqrt{16}}{\sqrt{8}}$

Step 3

Combine $\sqrt{16}$ and $\sqrt{8}$ into a single radical.

$\sqrt{\frac{16}{8}}$

Step 4

Divide $16$ by $8$ .

$\sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$