Simplify - square root of 9- square root of -81- square root of 16- square root of -4

$- \sqrt{9} - \sqrt{- 81} - \sqrt{16} - \sqrt{- 4}$

Step 1

Simplify each term.

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

$- \sqrt{3^{2}} - \sqrt{- 81} - \sqrt{16} - \sqrt{- 4}$

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

$- 1 \cdot 3 - \sqrt{- 81} - \sqrt{16} - \sqrt{- 4}$

Multiply $- 1$ by $3$ .

$- 3 - \sqrt{- 81} - \sqrt{16} - \sqrt{- 4}$

Rewrite $- 81$ as $- 1 (81)$ .

$- 3 - \sqrt{- 1 (81)} - \sqrt{16} - \sqrt{- 4}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$- 3 - (\sqrt{- 1} \cdot \sqrt{81}) - \sqrt{16} - \sqrt{- 4}$

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

$- 3 - (i \cdot \sqrt{81}) - \sqrt{16} - \sqrt{- 4}$

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

$- 3 - (i \cdot \sqrt{9^{2}}) - \sqrt{16} - \sqrt{- 4}$

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

$- 3 - (i \cdot 9) - \sqrt{16} - \sqrt{- 4}$

Move $9$ to the left of $i$ .

$- 3 - (9 \cdot i) - \sqrt{16} - \sqrt{- 4}$

Multiply $9$ by $- 1$ .

$- 3 - 9 i - \sqrt{16} - \sqrt{- 4}$

Rewrite $16$ as $4^{2}$ .

$- 3 - 9 i - \sqrt{4^{2}} - \sqrt{- 4}$

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

$- 3 - 9 i - 1 \cdot 4 - \sqrt{- 4}$

Multiply $- 1$ by $4$ .

$- 3 - 9 i - 4 - \sqrt{- 4}$

Rewrite $- 4$ as $- 1 (4)$ .

$- 3 - 9 i - 4 - \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- 3 - 9 i - 4 - (\sqrt{- 1} \cdot \sqrt{4})$

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

$- 3 - 9 i - 4 - (i \cdot \sqrt{4})$

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

$- 3 - 9 i - 4 - (i \cdot \sqrt{2^{2}})$

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

$- 3 - 9 i - 4 - (i \cdot 2)$

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

$- 3 - 9 i - 4 - (2 \cdot i)$

Multiply $2$ by $- 1$ .

$- 3 - 9 i - 4 - 2 i$

Step 2

Simplify by adding terms.

Subtract $4$ from $- 3$ .

$- 7 - 9 i - 2 i$

Subtract $2 i$ from $- 9 i$ .

$- 7 - 11 i$

Simplify - square root of 9- square root of -81- square root of 16- square root of -4

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