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Simplify ( square root of -48)/( square root of 2)

$\frac{\sqrt{- 48}}{\sqrt{2}}$

Step 1

Pull out imaginary unit

$i$ .

Rewrite

$- 48$ as

$- 1 (48)$ .

$\frac{\sqrt{- 1 (48)}}{\sqrt{2}}$

Rewrite

$\sqrt{- 1 (48)}$ as

$\sqrt{- 1} \cdot \sqrt{48}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{48}}{\sqrt{2}}$

Rewrite

$\sqrt{- 1}$ as

$i$ .

$\frac{i \cdot \sqrt{48}}{\sqrt{2}}$

$\frac{i \cdot \sqrt{48}}{\sqrt{2}}$

Step 2

Combine

$\sqrt{48}$ and

$\sqrt{2}$ into a single radical.

$i \cdot \sqrt{\frac{48}{2}}$

Step 3

Divide

$48$ by

$2$ .

$i \cdot \sqrt{24}$

Step 4

Rewrite

$24$ as

$2^{2} \cdot 6$ .

Factor

$4$ out of

$24$ .

$i \cdot \sqrt{4 (6)}$

Rewrite

$4$ as

$2^{2}$ .

$i \cdot \sqrt{2^{2} \cdot 6}$

$i \cdot \sqrt{2^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{6})$

Step 6

Move

$2$ to the left of

$i$ .

$2 i \sqrt{6}$

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