Simplify (14+ square root of -63)-( square root of 4928)

$(14 + \sqrt{- 63}) - (\sqrt{4928})$

Step 1

Simplify each term.

Rewrite $- 63$ as $- 1 (63)$ .

$14 + \sqrt{- 1 (63)} - (\sqrt{4928})$

Rewrite $\sqrt{- 1 (63)}$ as $\sqrt{- 1} \cdot \sqrt{63}$ .

$14 + \sqrt{- 1} \cdot \sqrt{63} - (\sqrt{4928})$

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

$14 + i \cdot \sqrt{63} - (\sqrt{4928})$

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$14 + i \cdot \sqrt{9 (7)} - (\sqrt{4928})$

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

$14 + i \cdot \sqrt{3^{2} \cdot 7} - (\sqrt{4928})$

Pull terms out from under the radical.

$14 + i \cdot (3 \sqrt{7}) - (\sqrt{4928})$

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

$14 + 3 \cdot i \sqrt{7} - (\sqrt{4928})$

Rewrite $4928$ as $8^{2} \cdot 77$ .

Factor $64$ out of $4928$ .

$14 + 3 i \sqrt{7} - \sqrt{64 (77)}$

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

$14 + 3 i \sqrt{7} - \sqrt{8^{2} \cdot 77}$

Pull terms out from under the radical.

$14 + 3 i \sqrt{7} - (8 \sqrt{77})$

Multiply $8$ by $- 1$ .

$14 + 3 i \sqrt{7} - 8 \sqrt{77}$

Step 2

Reorder $14 + 3 i \sqrt{7}$ and $- 8 \sqrt{77}$ .

$- 8 \sqrt{77} + 14 + 3 i \sqrt{7}$