Evaluate 8 square root of -72-3 square root of -128

$8 \sqrt{- 72} - 3 \sqrt{- 128}$

Step 1

Simplify each term.

Rewrite $- 72$ as $- 1 (72)$ .

$8 \sqrt{- 1 (72)} - 3 \sqrt{- 128}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$8 (\sqrt{- 1} \cdot \sqrt{72}) - 3 \sqrt{- 128}$

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

$8 (i \cdot \sqrt{72}) - 3 \sqrt{- 128}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$8 (i \cdot \sqrt{36 (2)}) - 3 \sqrt{- 128}$

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

$8 (i \cdot \sqrt{6^{2} \cdot 2}) - 3 \sqrt{- 128}$

Pull terms out from under the radical.

$8 (i \cdot (6 \sqrt{2})) - 3 \sqrt{- 128}$

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

$8 (6 \cdot i \sqrt{2}) - 3 \sqrt{- 128}$

Multiply $6$ by $8$ .

$48 (i \sqrt{2}) - 3 \sqrt{- 128}$

Rewrite $- 128$ as $- 1 (128)$ .

$48 i \sqrt{2} - 3 \sqrt{- 1 (128)}$

Rewrite $\sqrt{- 1 (128)}$ as $\sqrt{- 1} \cdot \sqrt{128}$ .

$48 i \sqrt{2} - 3 (\sqrt{- 1} \cdot \sqrt{128})$

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

$48 i \sqrt{2} - 3 (i \cdot \sqrt{128})$

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$48 i \sqrt{2} - 3 (i \cdot \sqrt{64 (2)})$

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

$48 i \sqrt{2} - 3 (i \cdot \sqrt{8^{2} \cdot 2})$

Pull terms out from under the radical.

$48 i \sqrt{2} - 3 (i \cdot (8 \sqrt{2}))$

Move $8$ to the left of $i$ .

$48 i \sqrt{2} - 3 (8 \cdot i \sqrt{2})$

Multiply $8$ by $- 3$ .

$48 i \sqrt{2} - 24 i \sqrt{2}$

Step 2

Subtract $24 i \sqrt{2}$ from $48 i \sqrt{2}$ .

$24 i \sqrt{2}$