Simplify 2 square root of -16- square root of 16-2 cube root of -216-3 cube root of -343

$2 \sqrt{- 16} - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Step 1

Simplify each term.

Rewrite $- 16$ as $- 1 (16)$ .

$2 \sqrt{- 1 (16)} - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$2 (\sqrt{- 1} \cdot \sqrt{16}) - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

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

$2 (i \cdot \sqrt{16}) - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Rewrite $16$ as $4^{2}$ .

$2 (i \cdot \sqrt{4^{2}}) - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

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

$2 (i \cdot 4) - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Move $4$ to the left of $i$ .

$2 (4 \cdot i) - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Multiply $4$ by $2$ .

$8 i - \sqrt{16} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Rewrite $16$ as $4^{2}$ .

$8 i - \sqrt{4^{2}} - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

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

$8 i - 1 \cdot 4 - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Multiply $- 1$ by $4$ .

$8 i - 4 - 2 \sqrt[3]{- 216} - 3 \sqrt[3]{- 343}$

Rewrite $- 216$ as ${(- 6)}^{3}$ .

$8 i - 4 - 2 \sqrt[3]{{(- 6)}^{3}} - 3 \sqrt[3]{- 343}$

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

$8 i - 4 - 2 \cdot - 6 - 3 \sqrt[3]{- 343}$

Multiply $- 2$ by $- 6$ .

$8 i - 4 + 12 - 3 \sqrt[3]{- 343}$

Rewrite $- 343$ as ${(- 7)}^{3}$ .

$8 i - 4 + 12 - 3 \sqrt[3]{{(- 7)}^{3}}$

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

$8 i - 4 + 12 - 3 \cdot - 7$

Multiply $- 3$ by $- 7$ .

$8 i - 4 + 12 + 21$

Step 2

Simplify the expression.

Add $- 4$ and $12$ .

$8 i + 8 + 21$

Add $8$ and $21$ .

$8 i + 29$

Reorder $8 i$ and $29$ .

$29 + 8 i$