Simplify - square root of 25+ square root of -40+ square root of 81- square root of -10

$- \sqrt{25} + \sqrt{- 40} + \sqrt{81} - \sqrt{- 10}$

Simplify each term.

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

$- \sqrt{5^{2}} + \sqrt{- 40} + \sqrt{81} - \sqrt{- 10}$

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

$- 1 \cdot 5 + \sqrt{- 40} + \sqrt{81} - \sqrt{- 10}$

Multiply $- 1$ by $5$ .

$- 5 + \sqrt{- 40} + \sqrt{81} - \sqrt{- 10}$

Rewrite $- 40$ as $- 1 (40)$ .

$- 5 + \sqrt{- 1 (40)} + \sqrt{81} - \sqrt{- 10}$

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$- 5 + \sqrt{- 1} \cdot \sqrt{40} + \sqrt{81} - \sqrt{- 10}$

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

$- 5 + i \cdot \sqrt{40} + \sqrt{81} - \sqrt{- 10}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$- 5 + i \cdot \sqrt{4 (10)} + \sqrt{81} - \sqrt{- 10}$

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

$- 5 + i \cdot \sqrt{2^{2} \cdot 10} + \sqrt{81} - \sqrt{- 10}$

Pull terms out from under the radical.

$- 5 + i \cdot (2 \sqrt{10}) + \sqrt{81} - \sqrt{- 10}$

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

$- 5 + 2 \cdot i \sqrt{10} + \sqrt{81} - \sqrt{- 10}$

Rewrite $81$ as $9^{2}$ .

$- 5 + 2 i \sqrt{10} + \sqrt{9^{2}} - \sqrt{- 10}$

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

$- 5 + 2 i \sqrt{10} + 9 - \sqrt{- 10}$

Rewrite $- 10$ as $- 1 (10)$ .

$- 5 + 2 i \sqrt{10} + 9 - \sqrt{- 1 (10)}$

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$- 5 + 2 i \sqrt{10} + 9 - (\sqrt{- 1} \cdot \sqrt{10})$

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

$- 5 + 2 i \sqrt{10} + 9 - i \sqrt{10}$

Simplify by adding terms.

Add $- 5$ and $9$ .

$2 i \sqrt{10} + 4 - i \sqrt{10}$

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

$1 i \sqrt{10} + 4$

Simplify the expression.

Multiply $i$ by $1$ .

$i \sqrt{10} + 4$

Reorder $i \sqrt{10}$ and $4$ .

$4 + i \sqrt{10}$