Simplify the Radical Expression square root of 121+ square root of -28- square root of 49- square root of -112

$\sqrt{121} + \sqrt{- 28} - \sqrt{49} - \sqrt{- 112}$

Simplify each term.

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2}} + \sqrt{- 28} - \sqrt{49} - \sqrt{- 112}$

Pull terms out from under the radical.

$| 11 | + \sqrt{- 28} - \sqrt{49} - \sqrt{- 112}$

The absolute value is the distance between a number and zero. The distance between $0$ and $11$ is $11$ .

$11 + \sqrt{- 28} - \sqrt{49} - \sqrt{- 112}$

Rewrite $- 28$ as $- 1 (28)$ .

$11 + \sqrt{- 1 (28)} - \sqrt{49} - \sqrt{- 112}$

Rewrite $\sqrt{- 1 (28)}$ as $\sqrt{- 1} \cdot \sqrt{28}$ .

$11 + \sqrt{- 1} \cdot \sqrt{28} - \sqrt{49} - \sqrt{- 112}$

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

$11 + i \cdot \sqrt{28} - \sqrt{49} - \sqrt{- 112}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$11 + i \cdot \sqrt{4 (7)} - \sqrt{49} - \sqrt{- 112}$

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

$11 + i \cdot \sqrt{2^{2} \cdot 7} - \sqrt{49} - \sqrt{- 112}$

Pull terms out from under the radical.

$11 + i \cdot (| 2 | \sqrt{7}) - \sqrt{49} - \sqrt{- 112}$

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

$11 + i \cdot (2 \sqrt{7}) - \sqrt{49} - \sqrt{- 112}$

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

$11 + 2 \cdot i \sqrt{7} - \sqrt{49} - \sqrt{- 112}$

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

$11 + 2 i \sqrt{7} - \sqrt{7^{2}} - \sqrt{- 112}$

Pull terms out from under the radical.

$11 + 2 i \sqrt{7} - | 7 | - \sqrt{- 112}$

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

$11 + 2 i \sqrt{7} - 1 \cdot 7 - \sqrt{- 112}$

Multiply $- 1$ by $7$ .

$11 + 2 i \sqrt{7} - 7 - \sqrt{- 112}$

Rewrite $- 112$ as $- 1 (112)$ .

$11 + 2 i \sqrt{7} - 7 - \sqrt{- 1 (112)}$

Rewrite $\sqrt{- 1 (112)}$ as $\sqrt{- 1} \cdot \sqrt{112}$ .

$11 + 2 i \sqrt{7} - 7 - (\sqrt{- 1} \cdot \sqrt{112})$

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

$11 + 2 i \sqrt{7} - 7 - (i \cdot \sqrt{112})$

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$11 + 2 i \sqrt{7} - 7 - (i \cdot \sqrt{16 (7)})$

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

$11 + 2 i \sqrt{7} - 7 - (i \cdot \sqrt{4^{2} \cdot 7})$

Pull terms out from under the radical.

$11 + 2 i \sqrt{7} - 7 - (i \cdot (| 4 | \sqrt{7}))$

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

$11 + 2 i \sqrt{7} - 7 - (i \cdot (4 \sqrt{7}))$

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

$11 + 2 i \sqrt{7} - 7 - (4 \cdot i \sqrt{7})$

Multiply $4$ by $- 1$ .

$11 + 2 i \sqrt{7} - 7 - 4 i \sqrt{7}$

Subtract $7$ from $11$ .

$2 i \sqrt{7} + 4 - 4 i \sqrt{7}$

Subtract $4 i \sqrt{7}$ from $2 i \sqrt{7}$ .

$- 2 i \sqrt{7} + 4$

Reorder $- 2 i \sqrt{7}$ and $4$ .

$4 - 2 i \sqrt{7}$

Simplify the Radical Expression square root of 121+ square root of -28- square root of 49- square root of -112

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