Simplify ( square root of -48)/( square root of -6)

$\frac{\sqrt{- 48}}{\sqrt{- 6}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 48$ as $- 1 (48)$ .

$\frac{\sqrt{- 1 (48)}}{\sqrt{- 6}}$

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{48}}{\sqrt{- 6}}$

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

$\frac{i \cdot \sqrt{48}}{\sqrt{- 6}}$

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{i \cdot \sqrt{48}}{\sqrt{- 1 (6)}}$

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$\frac{i \cdot \sqrt{48}}{\sqrt{- 1} \cdot \sqrt{6}}$

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

$\frac{i \cdot \sqrt{48}}{i \cdot \sqrt{6}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{48}}{i \cdot \sqrt{6}}$

Rewrite the expression.

$\frac{\sqrt{48}}{\sqrt{6}}$

Step 3

Combine $\sqrt{48}$ and $\sqrt{6}$ into a single radical.

$\sqrt{\frac{48}{6}}$

Step 4

Divide $48$ by $6$ .

$\sqrt{8}$

Step 5

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

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

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

Step 6

Pull terms out from under the radical.

$2 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$