Finite Math Examples

$\frac{\sqrt{- 48}}{\sqrt{3}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

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

$\frac{\sqrt{- 1 (48)}}{\sqrt{3}}$

Step 1.2

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

$\frac{\sqrt{- 1} \cdot \sqrt{48}}{\sqrt{3}}$

Step 1.3

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

$\frac{i \cdot \sqrt{48}}{\sqrt{3}}$

Step 2

Combine $\sqrt{48}$ and $\sqrt{3}$ into a single radical.

$i \cdot \sqrt{\frac{48}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Divide $48$ by $3$ .

$i \cdot \sqrt{16}$

Step 3.2

Rewrite $16$ as $4^{2}$ .

$i \cdot \sqrt{4^{2}}$

Step 3.3

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 4$

Step 3.4

Move $4$ to the left of $i$ .

$4 i$