Simplify - square root of 4+ square root of -28- square root of 64+ square root of -175

$- \sqrt{4} + \sqrt{- 28} - \sqrt{64} + \sqrt{- 175}$

Step 1

Simplify each term.

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

$- \sqrt{2^{2}} + \sqrt{- 28} - \sqrt{64} + \sqrt{- 175}$

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

$- 1 \cdot 2 + \sqrt{- 28} - \sqrt{64} + \sqrt{- 175}$

Multiply $- 1$ by $2$ .

$- 2 + \sqrt{- 28} - \sqrt{64} + \sqrt{- 175}$

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

$- 2 + \sqrt{- 1 (28)} - \sqrt{64} + \sqrt{- 175}$

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

$- 2 + \sqrt{- 1} \cdot \sqrt{28} - \sqrt{64} + \sqrt{- 175}$

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

$- 2 + i \cdot \sqrt{28} - \sqrt{64} + \sqrt{- 175}$

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

Factor $4$ out of $28$ .

$- 2 + i \cdot \sqrt{4 (7)} - \sqrt{64} + \sqrt{- 175}$

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

$- 2 + i \cdot \sqrt{2^{2} \cdot 7} - \sqrt{64} + \sqrt{- 175}$

Pull terms out from under the radical.

$- 2 + i \cdot (2 \sqrt{7}) - \sqrt{64} + \sqrt{- 175}$

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

$- 2 + 2 \cdot i \sqrt{7} - \sqrt{64} + \sqrt{- 175}$

Rewrite $64$ as $8^{2}$ .

$- 2 + 2 i \sqrt{7} - \sqrt{8^{2}} + \sqrt{- 175}$

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

$- 2 + 2 i \sqrt{7} - 1 \cdot 8 + \sqrt{- 175}$

Multiply $- 1$ by $8$ .

$- 2 + 2 i \sqrt{7} - 8 + \sqrt{- 175}$

Rewrite $- 175$ as $- 1 (175)$ .

$- 2 + 2 i \sqrt{7} - 8 + \sqrt{- 1 (175)}$

Rewrite $\sqrt{- 1 (175)}$ as $\sqrt{- 1} \cdot \sqrt{175}$ .

$- 2 + 2 i \sqrt{7} - 8 + \sqrt{- 1} \cdot \sqrt{175}$

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

$- 2 + 2 i \sqrt{7} - 8 + i \cdot \sqrt{175}$

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$- 2 + 2 i \sqrt{7} - 8 + i \cdot \sqrt{25 (7)}$

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

$- 2 + 2 i \sqrt{7} - 8 + i \cdot \sqrt{5^{2} \cdot 7}$

Pull terms out from under the radical.

$- 2 + 2 i \sqrt{7} - 8 + i \cdot (5 \sqrt{7})$

Move $5$ to the left of $i$ .

$- 2 + 2 i \sqrt{7} - 8 + 5 i \sqrt{7}$

Step 2

Simplify by adding terms.

Subtract $8$ from $- 2$ .

$2 i \sqrt{7} - 10 + 5 i \sqrt{7}$

Add $2 i \sqrt{7}$ and $5 i \sqrt{7}$ .

$7 i \sqrt{7} - 10$

Reorder $7 i \sqrt{7}$ and $- 10$ .

$- 10 + 7 i \sqrt{7}$

Simplify - square root of 4+ square root of -28- square root of 64+ square root of -175

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