Simplify square root of 36+ square root of -128- square root of 16+ square root of -98

$\sqrt{36} + \sqrt{- 128} - \sqrt{16} + \sqrt{- 98}$

Step 1

Simplify each term.

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}} + \sqrt{- 128} - \sqrt{16} + \sqrt{- 98}$

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

$6 + \sqrt{- 128} - \sqrt{16} + \sqrt{- 98}$

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

$6 + \sqrt{- 1 (128)} - \sqrt{16} + \sqrt{- 98}$

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

$6 + \sqrt{- 1} \cdot \sqrt{128} - \sqrt{16} + \sqrt{- 98}$

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

$6 + i \cdot \sqrt{128} - \sqrt{16} + \sqrt{- 98}$

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

Factor $64$ out of $128$ .

$6 + i \cdot \sqrt{64 (2)} - \sqrt{16} + \sqrt{- 98}$

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

$6 + i \cdot \sqrt{8^{2} \cdot 2} - \sqrt{16} + \sqrt{- 98}$

Pull terms out from under the radical.

$6 + i \cdot (8 \sqrt{2}) - \sqrt{16} + \sqrt{- 98}$

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

$6 + 8 \cdot i \sqrt{2} - \sqrt{16} + \sqrt{- 98}$

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

$6 + 8 i \sqrt{2} - \sqrt{4^{2}} + \sqrt{- 98}$

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

$6 + 8 i \sqrt{2} - 1 \cdot 4 + \sqrt{- 98}$

Multiply $- 1$ by $4$ .

$6 + 8 i \sqrt{2} - 4 + \sqrt{- 98}$

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

$6 + 8 i \sqrt{2} - 4 + \sqrt{- 1 (98)}$

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

$6 + 8 i \sqrt{2} - 4 + \sqrt{- 1} \cdot \sqrt{98}$

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

$6 + 8 i \sqrt{2} - 4 + i \cdot \sqrt{98}$

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

Factor $49$ out of $98$ .

$6 + 8 i \sqrt{2} - 4 + i \cdot \sqrt{49 (2)}$

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

$6 + 8 i \sqrt{2} - 4 + i \cdot \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$6 + 8 i \sqrt{2} - 4 + i \cdot (7 \sqrt{2})$

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

$6 + 8 i \sqrt{2} - 4 + 7 i \sqrt{2}$

Step 2

Simplify by adding terms.

Subtract $4$ from $6$ .

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

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

$15 i \sqrt{2} + 2$

Reorder $15 i \sqrt{2}$ and $2$ .

$2 + 15 i \sqrt{2}$

Simplify square root of 36+ square root of -128- square root of 16+ square root of -98

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