Simplify (- square root of 9+ square root of -4)-(2 square root of 576+ square root of -64)

$(- \sqrt{9} + \sqrt{- 4}) - (2 \sqrt{576} + \sqrt{- 64})$

Step 1

Simplify each term.

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

$- \sqrt{3^{2}} + \sqrt{- 4} - (2 \sqrt{576} + \sqrt{- 64})$

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

$- 1 \cdot 3 + \sqrt{- 4} - (2 \sqrt{576} + \sqrt{- 64})$

Multiply $- 1$ by $3$ .

$- 3 + \sqrt{- 4} - (2 \sqrt{576} + \sqrt{- 64})$

Rewrite $- 4$ as $- 1 (4)$ .

$- 3 + \sqrt{- 1 (4)} - (2 \sqrt{576} + \sqrt{- 64})$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- 3 + \sqrt{- 1} \cdot \sqrt{4} - (2 \sqrt{576} + \sqrt{- 64})$

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

$- 3 + i \cdot \sqrt{4} - (2 \sqrt{576} + \sqrt{- 64})$

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

$- 3 + i \cdot \sqrt{2^{2}} - (2 \sqrt{576} + \sqrt{- 64})$

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

$- 3 + i \cdot 2 - (2 \sqrt{576} + \sqrt{- 64})$

Move $2$ to the left of $i$ .

$- 3 + 2 \cdot i - (2 \sqrt{576} + \sqrt{- 64})$

Rewrite $- 64$ as $- 1 (64)$ .

$- 3 + 2 i - (2 \sqrt{576} + \sqrt{- 1 (64)})$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$- 3 + 2 i - (2 \sqrt{576} + \sqrt{- 1} \cdot \sqrt{64})$

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

$- 3 + 2 i - (2 \sqrt{576} + i \cdot \sqrt{64})$

Simplify each term.

Rewrite $576$ as $24^{2}$ .

$- 3 + 2 i - (2 \sqrt{24^{2}} + i \cdot \sqrt{64})$

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

$- 3 + 2 i - (2 \cdot 24 + i \cdot \sqrt{64})$

Multiply $2$ by $24$ .

$- 3 + 2 i - (48 + i \cdot \sqrt{64})$

Rewrite $64$ as $8^{2}$ .

$- 3 + 2 i - (48 + i \cdot \sqrt{8^{2}})$

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

$- 3 + 2 i - (48 + i \cdot 8)$

Move $8$ to the left of $i$ .

$- 3 + 2 i - (48 + 8 i)$

Apply the distributive property.

$- 3 + 2 i - 1 \cdot 48 - (8 i)$

Multiply $- 1$ by $48$ .

$- 3 + 2 i - 48 - (8 i)$

Multiply $8$ by $- 1$ .

$- 3 + 2 i - 48 - 8 i$

Step 2

Simplify by adding terms.

Subtract $48$ from $- 3$ .

$- 51 + 2 i - 8 i$

Subtract $8 i$ from $2 i$ .

$- 51 - 6 i$

Simplify (- square root of 9+ square root of -4)-(2 square root of 576+ square root of -64)

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