Evaluate (6-2 square root of -49)-(4+ square root of -9)

$(6 - 2 \sqrt{- 49}) - (4 + \sqrt{- 9})$

Step 1

Simplify each term.

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

$6 - 2 \sqrt{- 1 (49)} - (4 + \sqrt{- 9})$

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

$6 - 2 (\sqrt{- 1} \cdot \sqrt{49}) - (4 + \sqrt{- 9})$

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

$6 - 2 (i \cdot \sqrt{49}) - (4 + \sqrt{- 9})$

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

$6 - 2 (i \cdot \sqrt{7^{2}}) - (4 + \sqrt{- 9})$

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

$6 - 2 (i \cdot 7) - (4 + \sqrt{- 9})$

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

$6 - 2 (7 \cdot i) - (4 + \sqrt{- 9})$

Multiply $7$ by $- 2$ .

$6 - 14 i - (4 + \sqrt{- 9})$

Rewrite $- 9$ as $- 1 (9)$ .

$6 - 14 i - (4 + \sqrt{- 1 (9)})$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$6 - 14 i - (4 + \sqrt{- 1} \cdot \sqrt{9})$

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

$6 - 14 i - (4 + i \cdot \sqrt{9})$

Simplify each term.

Rewrite $9$ as $3^{2}$ .

$6 - 14 i - (4 + i \cdot \sqrt{3^{2}})$

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

$6 - 14 i - (4 + i \cdot 3)$

Move $3$ to the left of $i$ .

$6 - 14 i - (4 + 3 i)$

Apply the distributive property.

$6 - 14 i - 1 \cdot 4 - (3 i)$

Multiply $- 1$ by $4$ .

$6 - 14 i - 4 - (3 i)$

Multiply $3$ by $- 1$ .

$6 - 14 i - 4 - 3 i$

Step 2

Simplify by adding terms.

Subtract $4$ from $6$ .

$2 - 14 i - 3 i$

Subtract $3 i$ from $- 14 i$ .

$2 - 17 i$