Simplify - square root of 121+ square root of -200+ square root of 9- square root of -98

$- \sqrt{121} + \sqrt{- 200} + \sqrt{9} - \sqrt{- 98}$

Simplify each term.

Rewrite $121$ as $11^{2}$ .

$- \sqrt{11^{2}} + \sqrt{- 200} + \sqrt{9} - \sqrt{- 98}$

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

$- 1 \cdot 11 + \sqrt{- 200} + \sqrt{9} - \sqrt{- 98}$

Multiply $- 1$ by $11$ .

$- 11 + \sqrt{- 200} + \sqrt{9} - \sqrt{- 98}$

Rewrite $- 200$ as $- 1 (200)$ .

$- 11 + \sqrt{- 1 (200)} + \sqrt{9} - \sqrt{- 98}$

Rewrite $\sqrt{- 1 (200)}$ as $\sqrt{- 1} \cdot \sqrt{200}$ .

$- 11 + \sqrt{- 1} \cdot \sqrt{200} + \sqrt{9} - \sqrt{- 98}$

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

$- 11 + i \cdot \sqrt{200} + \sqrt{9} - \sqrt{- 98}$

Rewrite $200$ as $10^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$- 11 + i \cdot \sqrt{100 (2)} + \sqrt{9} - \sqrt{- 98}$

Rewrite $100$ as $10^{2}$ .

$- 11 + i \cdot \sqrt{10^{2} \cdot 2} + \sqrt{9} - \sqrt{- 98}$

Pull terms out from under the radical.

$- 11 + i \cdot (10 \sqrt{2}) + \sqrt{9} - \sqrt{- 98}$

Move $10$ to the left of $i$ .

$- 11 + 10 \cdot i \sqrt{2} + \sqrt{9} - \sqrt{- 98}$

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

$- 11 + 10 i \sqrt{2} + \sqrt{3^{2}} - \sqrt{- 98}$

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

$- 11 + 10 i \sqrt{2} + 3 - \sqrt{- 98}$

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

$- 11 + 10 i \sqrt{2} + 3 - \sqrt{- 1 (98)}$

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

$- 11 + 10 i \sqrt{2} + 3 - (\sqrt{- 1} \cdot \sqrt{98})$

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

$- 11 + 10 i \sqrt{2} + 3 - (i \cdot \sqrt{98})$

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

Factor $49$ out of $98$ .

$- 11 + 10 i \sqrt{2} + 3 - (i \cdot \sqrt{49 (2)})$

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

$- 11 + 10 i \sqrt{2} + 3 - (i \cdot \sqrt{7^{2} \cdot 2})$

Pull terms out from under the radical.

$- 11 + 10 i \sqrt{2} + 3 - (i \cdot (7 \sqrt{2}))$

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

$- 11 + 10 i \sqrt{2} + 3 - (7 \cdot i \sqrt{2})$

Multiply $7$ by $- 1$ .

$- 11 + 10 i \sqrt{2} + 3 - 7 i \sqrt{2}$

Simplify by adding terms.

Add $- 11$ and $3$ .

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

Subtract $7 i \sqrt{2}$ from $10 i \sqrt{2}$ .

$3 i \sqrt{2} - 8$

Reorder $3 i \sqrt{2}$ and $- 8$ .

$- 8 + 3 i \sqrt{2}$

Simplify - square root of 121+ square root of -200+ square root of 9- square root of -98

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