Write in Standard Form (6+ square root of -48)/2

$\frac{6 + \sqrt{- 48}}{2}$

Step 1

Pull out imaginary unit $i$ .

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

$\frac{6 + \sqrt{- 1 (48)}}{2}$

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

$\frac{6 + \sqrt{- 1} \cdot \sqrt{48}}{2}$

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

$\frac{6 + i \cdot \sqrt{48}}{2}$

Step 2

Simplify the numerator.

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$\frac{6 + i \cdot \sqrt{16 (3)}}{2}$

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

$\frac{6 + i \cdot \sqrt{4^{2} \cdot 3}}{2}$

Pull terms out from under the radical.

$\frac{6 + i \cdot (4 \sqrt{3})}{2}$

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

$\frac{6 + 4 i \sqrt{3}}{2}$

Step 3

Cancel the common factor of $6 + 4 i \sqrt{3}$ and $2$ .

Factor $2$ out of $6$ .

$\frac{2 \cdot 3 + 4 i \sqrt{3}}{2}$

Factor $2$ out of $4 i \sqrt{3}$ .

$\frac{2 \cdot 3 + 2 (2 i \sqrt{3})}{2}$

Factor $2$ out of $2 (3) + 2 (2 i \sqrt{3})$ .

$\frac{2 (3 + 2 i \sqrt{3})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (3 + 2 i \sqrt{3})}{2 (1)}$

Cancel the common factor.

$\frac{2 (3 + 2 i \sqrt{3})}{2 \cdot 1}$

Rewrite the expression.

$\frac{3 + 2 i \sqrt{3}}{1}$

Divide $3 + 2 i \sqrt{3}$ by $1$ .

$3 + 2 i \sqrt{3}$