Simplify - square root of 64+ square root of -36- square root of 4- square root of -1

$- \sqrt{64} + \sqrt{- 36} - \sqrt{4} - \sqrt{- 1}$

Step 1

Simplify each term.

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

$- \sqrt{8^{2}} + \sqrt{- 36} - \sqrt{4} - \sqrt{- 1}$

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

$- 1 \cdot 8 + \sqrt{- 36} - \sqrt{4} - \sqrt{- 1}$

Multiply $- 1$ by $8$ .

$- 8 + \sqrt{- 36} - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + \sqrt{- 1 (36)} - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + \sqrt{- 1} \cdot \sqrt{36} - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + i \cdot \sqrt{36} - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + i \cdot \sqrt{6^{2}} - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + i \cdot 6 - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + 6 \cdot i - \sqrt{4} - \sqrt{- 1}$

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

$- 8 + 6 i - \sqrt{2^{2}} - \sqrt{- 1}$

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

$- 8 + 6 i - 1 \cdot 2 - \sqrt{- 1}$

Multiply $- 1$ by $2$ .

$- 8 + 6 i - 2 - \sqrt{- 1}$

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

$- 8 + 6 i - 2 - i$

Step 2

Simplify by adding terms.

Subtract $2$ from $- 8$ .

$- 10 + 6 i - i$

Subtract $i$ from $6 i$ .

$- 10 + 5 i$