Simplify the Radical Expression square root of 4+ square root of -36- square root of 49+ square root of -49

$\sqrt{4} + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Simplify each term.

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

$\sqrt{2^{2}} + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Pull terms out from under the radical.

$| 2 | + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$2 + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Rewrite $- 36$ as $- 1 (36)$ .

$2 + \sqrt{- 1 (36)} - \sqrt{49} + \sqrt{- 49}$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$2 + \sqrt{- 1} \cdot \sqrt{36} - \sqrt{49} + \sqrt{- 49}$

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

$2 + i \cdot \sqrt{36} - \sqrt{49} + \sqrt{- 49}$

Rewrite $36$ as $6^{2}$ .

$2 + i \cdot \sqrt{6^{2}} - \sqrt{49} + \sqrt{- 49}$

Pull terms out from under the radical.

$2 + i \cdot | 6 | - \sqrt{49} + \sqrt{- 49}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$2 + i \cdot 6 - \sqrt{49} + \sqrt{- 49}$

Move $6$ to the left of $i$ .

$2 + 6 \cdot i - \sqrt{49} + \sqrt{- 49}$

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

$2 + 6 i - \sqrt{7^{2}} + \sqrt{- 49}$

Pull terms out from under the radical.

$2 + 6 i - | 7 | + \sqrt{- 49}$

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

$2 + 6 i - 1 \cdot 7 + \sqrt{- 49}$

Multiply $- 1$ by $7$ .

$2 + 6 i - 7 + \sqrt{- 49}$

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

$2 + 6 i - 7 + \sqrt{- 1 (49)}$

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

$2 + 6 i - 7 + \sqrt{- 1} \cdot \sqrt{49}$

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

$2 + 6 i - 7 + i \cdot \sqrt{49}$

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

$2 + 6 i - 7 + i \cdot \sqrt{7^{2}}$

Pull terms out from under the radical.

$2 + 6 i - 7 + i \cdot | 7 |$

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

$2 + 6 i - 7 + i \cdot 7$

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

$2 + 6 i - 7 + 7 i$

Subtract $7$ from $2$ .

$- 5 + 6 i + 7 i$

Add $6 i$ and $7 i$ .

$- 5 + 13 i$

Simplify the Radical Expression square root of 4+ square root of -36- square root of 49+ square root of -49

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