Simplify - square root of 4+ square root of -200- square root of 1+ square root of -18

$- \sqrt{4} + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Simplify each term.

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

$- \sqrt{2^{2}} + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

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

$- 1 \cdot 2 + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Multiply $- 1$ by $2$ .

$- 2 + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

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

$- 2 + \sqrt{- 1 (200)} - \sqrt{1} + \sqrt{- 18}$

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

$- 2 + \sqrt{- 1} \cdot \sqrt{200} - \sqrt{1} + \sqrt{- 18}$

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

$- 2 + i \cdot \sqrt{200} - \sqrt{1} + \sqrt{- 18}$

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

Factor $100$ out of $200$ .

$- 2 + i \cdot \sqrt{100 (2)} - \sqrt{1} + \sqrt{- 18}$

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

$- 2 + i \cdot \sqrt{10^{2} \cdot 2} - \sqrt{1} + \sqrt{- 18}$

Pull terms out from under the radical.

$- 2 + i \cdot (10 \sqrt{2}) - \sqrt{1} + \sqrt{- 18}$

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

$- 2 + 10 \cdot i \sqrt{2} - \sqrt{1} + \sqrt{- 18}$

Any root of $1$ is $1$ .

$- 2 + 10 i \sqrt{2} - 1 \cdot 1 + \sqrt{- 18}$

Multiply $- 1$ by $1$ .

$- 2 + 10 i \sqrt{2} - 1 + \sqrt{- 18}$

Rewrite $- 18$ as $- 1 (18)$ .

$- 2 + 10 i \sqrt{2} - 1 + \sqrt{- 1 (18)}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$- 2 + 10 i \sqrt{2} - 1 + \sqrt{- 1} \cdot \sqrt{18}$

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

$- 2 + 10 i \sqrt{2} - 1 + i \cdot \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$- 2 + 10 i \sqrt{2} - 1 + i \cdot \sqrt{9 (2)}$

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

$- 2 + 10 i \sqrt{2} - 1 + i \cdot \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

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

Move $3$ to the left of $i$ .

$- 2 + 10 i \sqrt{2} - 1 + 3 i \sqrt{2}$

Simplify by adding terms.

Subtract $1$ from $- 2$ .

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

Add $10 i \sqrt{2}$ and $3 i \sqrt{2}$ .

$13 i \sqrt{2} - 3$

Reorder $13 i \sqrt{2}$ and $- 3$ .

$- 3 + 13 i \sqrt{2}$

Simplify - square root of 4+ square root of -200- square root of 1+ square root of -18

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