Simplify square root of -27+ square root of -48

$\sqrt{- 27} + \sqrt{- 48}$

Simplify each term.

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Rewrite $- 27$ as $- 1 (27)$ .

$\sqrt{- 1 (27)} + \sqrt{- 48}$

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$\sqrt{- 1} \cdot \sqrt{27} + \sqrt{- 48}$

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

$i \cdot \sqrt{27} + \sqrt{- 48}$

Rewrite $27$ as $3^{2} \cdot 3$ .

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Factor $9$ out of $27$ .

$i \cdot \sqrt{9 (3)} + \sqrt{- 48}$

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2} \cdot 3} + \sqrt{- 48}$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{3}) + \sqrt{- 48}$

Move $3$ to the left of $i$ .

$3 \cdot i \sqrt{3} + \sqrt{- 48}$

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

$3 i \sqrt{3} + \sqrt{- 1 (48)}$

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

$3 i \sqrt{3} + \sqrt{- 1} \cdot \sqrt{48}$

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

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

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

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Factor $16$ out of $48$ .

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

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

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

Pull terms out from under the radical.

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

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

$3 i \sqrt{3} + 4 i \sqrt{3}$

Add $3 i \sqrt{3}$ and $4 i \sqrt{3}$ .

$7 i \sqrt{3}$

Simplify square root of -27+ square root of -48