Simplify the Radical Expression - square root of 81+ square root of -49+ square root of 25+ square root of -1

$- \sqrt{81} + \sqrt{- 49} + \sqrt{25} + \sqrt{- 1}$

Step 1

Simplify each term.

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

$- \sqrt{9^{2}} + \sqrt{- 49} + \sqrt{25} + \sqrt{- 1}$

Pull terms out from under the radical.

$- | 9 | + \sqrt{- 49} + \sqrt{25} + \sqrt{- 1}$

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

$- 1 \cdot 9 + \sqrt{- 49} + \sqrt{25} + \sqrt{- 1}$

Multiply $- 1$ by $9$ .

$- 9 + \sqrt{- 49} + \sqrt{25} + \sqrt{- 1}$

Rewrite $- 49$ as $- 1 (49)$ .

$- 9 + \sqrt{- 1 (49)} + \sqrt{25} + \sqrt{- 1}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$- 9 + \sqrt{- 1} \cdot \sqrt{49} + \sqrt{25} + \sqrt{- 1}$

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

$- 9 + i \cdot \sqrt{49} + \sqrt{25} + \sqrt{- 1}$

Rewrite $49$ as $7^{2}$ .

$- 9 + i \cdot \sqrt{7^{2}} + \sqrt{25} + \sqrt{- 1}$

Pull terms out from under the radical.

$- 9 + i \cdot | 7 | + \sqrt{25} + \sqrt{- 1}$

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$- 9 + i \cdot 7 + \sqrt{25} + \sqrt{- 1}$

Move $7$ to the left of $i$ .

$- 9 + 7 \cdot i + \sqrt{25} + \sqrt{- 1}$

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

$- 9 + 7 i + \sqrt{5^{2}} + \sqrt{- 1}$

Pull terms out from under the radical.

$- 9 + 7 i + | 5 | + \sqrt{- 1}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$- 9 + 7 i + 5 + \sqrt{- 1}$

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

$- 9 + 7 i + 5 + i$

Step 2

Add $- 9$ and $5$ .

$- 4 + 7 i + i$

Step 3

Add $7 i$ and $i$ .

$- 4 + 8 i$