Simplify square root of 4- square root of -98- square root of 144+ square root of -128

$\sqrt{4} - \sqrt{- 98} - \sqrt{144} + \sqrt{- 128}$

Step 1

Simplify each term.

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

$\sqrt{2^{2}} - \sqrt{- 98} - \sqrt{144} + \sqrt{- 128}$

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

$2 - \sqrt{- 98} - \sqrt{144} + \sqrt{- 128}$

Rewrite $- 98$ as $- 1 (98)$ .

$2 - \sqrt{- 1 (98)} - \sqrt{144} + \sqrt{- 128}$

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$2 - (\sqrt{- 1} \cdot \sqrt{98}) - \sqrt{144} + \sqrt{- 128}$

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

$2 - (i \cdot \sqrt{98}) - \sqrt{144} + \sqrt{- 128}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$2 - (i \cdot \sqrt{49 (2)}) - \sqrt{144} + \sqrt{- 128}$

Rewrite $49$ as $7^{2}$ .

$2 - (i \cdot \sqrt{7^{2} \cdot 2}) - \sqrt{144} + \sqrt{- 128}$

Pull terms out from under the radical.

$2 - (i \cdot (7 \sqrt{2})) - \sqrt{144} + \sqrt{- 128}$

Move $7$ to the left of $i$ .

$2 - (7 \cdot i \sqrt{2}) - \sqrt{144} + \sqrt{- 128}$

Multiply $7$ by $- 1$ .

$2 - 7 (i \sqrt{2}) - \sqrt{144} + \sqrt{- 128}$

Rewrite $144$ as $12^{2}$ .

$2 - 7 i \sqrt{2} - \sqrt{12^{2}} + \sqrt{- 128}$

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

$2 - 7 i \sqrt{2} - 1 \cdot 12 + \sqrt{- 128}$

Multiply $- 1$ by $12$ .

$2 - 7 i \sqrt{2} - 12 + \sqrt{- 128}$

Rewrite $- 128$ as $- 1 (128)$ .

$2 - 7 i \sqrt{2} - 12 + \sqrt{- 1 (128)}$

Rewrite $\sqrt{- 1 (128)}$ as $\sqrt{- 1} \cdot \sqrt{128}$ .

$2 - 7 i \sqrt{2} - 12 + \sqrt{- 1} \cdot \sqrt{128}$

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

$2 - 7 i \sqrt{2} - 12 + i \cdot \sqrt{128}$

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$2 - 7 i \sqrt{2} - 12 + i \cdot \sqrt{64 (2)}$

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

$2 - 7 i \sqrt{2} - 12 + i \cdot \sqrt{8^{2} \cdot 2}$

Pull terms out from under the radical.

$2 - 7 i \sqrt{2} - 12 + i \cdot (8 \sqrt{2})$

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

$2 - 7 i \sqrt{2} - 12 + 8 i \sqrt{2}$

Step 2

Simplify by adding terms.

Subtract $12$ from $2$ .

$- 7 i \sqrt{2} - 10 + 8 i \sqrt{2}$

Add $- 7 i \sqrt{2}$ and $8 i \sqrt{2}$ .

$1 i \sqrt{2} - 10$

Simplify the expression.

Multiply $i$ by $1$ .

$i \sqrt{2} - 10$

Reorder $i \sqrt{2}$ and $- 10$ .

$- 10 + i \sqrt{2}$

Simplify square root of 4- square root of -98- square root of 144+ square root of -128

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