Simplify the Radical Expression - square root of 81+ square root of -9+ square root of 144+ square root of -16

$- \sqrt{81} + \sqrt{- 9} + \sqrt{144} + \sqrt{- 16}$

Simplify each term.

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

$- \sqrt{9^{2}} + \sqrt{- 9} + \sqrt{144} + \sqrt{- 16}$

Pull terms out from under the radical.

$- | 9 | + \sqrt{- 9} + \sqrt{144} + \sqrt{- 16}$

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$- 1 \cdot 9 + \sqrt{- 9} + \sqrt{144} + \sqrt{- 16}$

Multiply $- 1$ by $9$ .

$- 9 + \sqrt{- 9} + \sqrt{144} + \sqrt{- 16}$

Rewrite $- 9$ as $- 1 (9)$ .

$- 9 + \sqrt{- 1 (9)} + \sqrt{144} + \sqrt{- 16}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$- 9 + \sqrt{- 1} \cdot \sqrt{9} + \sqrt{144} + \sqrt{- 16}$

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

$- 9 + i \cdot \sqrt{9} + \sqrt{144} + \sqrt{- 16}$

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

$- 9 + i \cdot \sqrt{3^{2}} + \sqrt{144} + \sqrt{- 16}$

Pull terms out from under the radical.

$- 9 + i \cdot | 3 | + \sqrt{144} + \sqrt{- 16}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$- 9 + i \cdot 3 + \sqrt{144} + \sqrt{- 16}$

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

$- 9 + 3 \cdot i + \sqrt{144} + \sqrt{- 16}$

Rewrite $144$ as $12^{2}$ .

$- 9 + 3 i + \sqrt{12^{2}} + \sqrt{- 16}$

Pull terms out from under the radical.

$- 9 + 3 i + | 12 | + \sqrt{- 16}$

The absolute value is the distance between a number and zero. The distance between $0$ and $12$ is $12$ .

$- 9 + 3 i + 12 + \sqrt{- 16}$

Rewrite $- 16$ as $- 1 (16)$ .

$- 9 + 3 i + 12 + \sqrt{- 1 (16)}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$- 9 + 3 i + 12 + \sqrt{- 1} \cdot \sqrt{16}$

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

$- 9 + 3 i + 12 + i \cdot \sqrt{16}$

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

$- 9 + 3 i + 12 + i \cdot \sqrt{4^{2}}$

Pull terms out from under the radical.

$- 9 + 3 i + 12 + i \cdot | 4 |$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$- 9 + 3 i + 12 + i \cdot 4$

Move $4$ to the left of $i$ .

$- 9 + 3 i + 12 + 4 i$

Add $- 9$ and $12$ .

$3 + 3 i + 4 i$

Add $3 i$ and $4 i$ .

$3 + 7 i$

Simplify the Radical Expression - square root of 81+ square root of -9+ square root of 144+ square root of -16

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