Simplify square root of 9- square root of -200+ square root of 121- square root of -50

$\sqrt{9} - \sqrt{- 200} + \sqrt{121} - \sqrt{- 50}$

Simplify each term.

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

$\sqrt{3^{2}} - \sqrt{- 200} + \sqrt{121} - \sqrt{- 50}$

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

$3 - \sqrt{- 200} + \sqrt{121} - \sqrt{- 50}$

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

$3 - \sqrt{- 1 (200)} + \sqrt{121} - \sqrt{- 50}$

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

$3 - (\sqrt{- 1} \cdot \sqrt{200}) + \sqrt{121} - \sqrt{- 50}$

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

$3 - (i \cdot \sqrt{200}) + \sqrt{121} - \sqrt{- 50}$

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

Factor $100$ out of $200$ .

$3 - (i \cdot \sqrt{100 (2)}) + \sqrt{121} - \sqrt{- 50}$

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

$3 - (i \cdot \sqrt{10^{2} \cdot 2}) + \sqrt{121} - \sqrt{- 50}$

Pull terms out from under the radical.

$3 - (i \cdot (10 \sqrt{2})) + \sqrt{121} - \sqrt{- 50}$

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

$3 - (10 \cdot i \sqrt{2}) + \sqrt{121} - \sqrt{- 50}$

Multiply $10$ by $- 1$ .

$3 - 10 (i \sqrt{2}) + \sqrt{121} - \sqrt{- 50}$

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

$3 - 10 i \sqrt{2} + \sqrt{11^{2}} - \sqrt{- 50}$

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

$3 - 10 i \sqrt{2} + 11 - \sqrt{- 50}$

Rewrite $- 50$ as $- 1 (50)$ .

$3 - 10 i \sqrt{2} + 11 - \sqrt{- 1 (50)}$

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$3 - 10 i \sqrt{2} + 11 - (\sqrt{- 1} \cdot \sqrt{50})$

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

$3 - 10 i \sqrt{2} + 11 - (i \cdot \sqrt{50})$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$3 - 10 i \sqrt{2} + 11 - (i \cdot \sqrt{25 (2)})$

Rewrite $25$ as $5^{2}$ .

$3 - 10 i \sqrt{2} + 11 - (i \cdot \sqrt{5^{2} \cdot 2})$

Pull terms out from under the radical.

$3 - 10 i \sqrt{2} + 11 - (i \cdot (5 \sqrt{2}))$

Move $5$ to the left of $i$ .

$3 - 10 i \sqrt{2} + 11 - (5 \cdot i \sqrt{2})$

Multiply $5$ by $- 1$ .

$3 - 10 i \sqrt{2} + 11 - 5 i \sqrt{2}$

Simplify by adding terms.

Add $3$ and $11$ .

$- 10 i \sqrt{2} + 14 - 5 i \sqrt{2}$

Subtract $5 i \sqrt{2}$ from $- 10 i \sqrt{2}$ .

$- 15 i \sqrt{2} + 14$

Reorder $- 15 i \sqrt{2}$ and $14$ .

$14 - 15 i \sqrt{2}$

Simplify square root of 9- square root of -200+ square root of 121- square root of -50

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