Write in Standard Form (-2+ square root of -8)+(5- square root of -50)

$(- 2 + \sqrt{- 8}) + (5 - \sqrt{- 50})$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Simplify each term.

Rewrite $- 8$ as $- 1 (8)$ .

$- 2 + \sqrt{- 1 (8)} + 5 - \sqrt{- 50}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$- 2 + \sqrt{- 1} \cdot \sqrt{8} + 5 - \sqrt{- 50}$

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

$- 2 + i \cdot \sqrt{8} + 5 - \sqrt{- 50}$

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

Factor $4$ out of $8$ .

$- 2 + i \cdot \sqrt{4 (2)} + 5 - \sqrt{- 50}$

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

$- 2 + i \cdot \sqrt{2^{2} \cdot 2} + 5 - \sqrt{- 50}$

Pull terms out from under the radical.

$- 2 + i \cdot (2 \sqrt{2}) + 5 - \sqrt{- 50}$

Move $2$ to the left of $i$ .

$- 2 + 2 \cdot i \sqrt{2} + 5 - \sqrt{- 50}$

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

$- 2 + 2 i \sqrt{2} + 5 - \sqrt{- 1 (50)}$

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

$- 2 + 2 i \sqrt{2} + 5 - (\sqrt{- 1} \cdot \sqrt{50})$

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

$- 2 + 2 i \sqrt{2} + 5 - (i \cdot \sqrt{50})$

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

Factor $25$ out of $50$ .

$- 2 + 2 i \sqrt{2} + 5 - (i \cdot \sqrt{25 (2)})$

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

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

Pull terms out from under the radical.

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

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

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

Multiply $5$ by $- 1$ .

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

Simplify by adding terms.

Add $- 2$ and $5$ .

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

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

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

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

$3 - 3 i \sqrt{2}$