Simplify - square root of 81- square root of -25+ square root of 100- square root of -1

$- \sqrt{81} - \sqrt{- 25} + \sqrt{100} - \sqrt{- 1}$

Step 1

Simplify each term.

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

$- \sqrt{9^{2}} - \sqrt{- 25} + \sqrt{100} - \sqrt{- 1}$

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

$- 1 \cdot 9 - \sqrt{- 25} + \sqrt{100} - \sqrt{- 1}$

Multiply $- 1$ by $9$ .

$- 9 - \sqrt{- 25} + \sqrt{100} - \sqrt{- 1}$

Rewrite $- 25$ as $- 1 (25)$ .

$- 9 - \sqrt{- 1 (25)} + \sqrt{100} - \sqrt{- 1}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$- 9 - (\sqrt{- 1} \cdot \sqrt{25}) + \sqrt{100} - \sqrt{- 1}$

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

$- 9 - (i \cdot \sqrt{25}) + \sqrt{100} - \sqrt{- 1}$

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

$- 9 - (i \cdot \sqrt{5^{2}}) + \sqrt{100} - \sqrt{- 1}$

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

$- 9 - (i \cdot 5) + \sqrt{100} - \sqrt{- 1}$

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

$- 9 - (5 \cdot i) + \sqrt{100} - \sqrt{- 1}$

Multiply $5$ by $- 1$ .

$- 9 - 5 i + \sqrt{100} - \sqrt{- 1}$

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

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

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

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

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

$- 9 - 5 i + 10 - i$

Step 2

Simplify by adding terms.

Add $- 9$ and $10$ .

$1 - 5 i - i$

Subtract $i$ from $- 5 i$ .

$1 - 6 i$