Simplify -3 square root of -4-4 square root of -4-2 cube root of -64

$- 3 \sqrt{- 4} - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

Simplify each term.

Rewrite $- 4$ as $- 1 (4)$ .

$- 3 \sqrt{- 1 (4)} - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- 3 (\sqrt{- 1} \cdot \sqrt{4}) - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

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

$- 3 (i \cdot \sqrt{4}) - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

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

$- 3 (i \cdot \sqrt{2^{2}}) - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

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

$- 3 (i \cdot 2) - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

Move $2$ to the left of $i$ .

$- 3 (2 \cdot i) - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

Multiply $2$ by $- 3$ .

$- 6 i - 4 \sqrt{- 4} - 2 \sqrt[3]{- 64}$

Rewrite $- 4$ as $- 1 (4)$ .

$- 6 i - 4 \sqrt{- 1 (4)} - 2 \sqrt[3]{- 64}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- 6 i - 4 (\sqrt{- 1} \cdot \sqrt{4}) - 2 \sqrt[3]{- 64}$

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

$- 6 i - 4 (i \cdot \sqrt{4}) - 2 \sqrt[3]{- 64}$

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

$- 6 i - 4 (i \cdot \sqrt{2^{2}}) - 2 \sqrt[3]{- 64}$

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

$- 6 i - 4 (i \cdot 2) - 2 \sqrt[3]{- 64}$

Move $2$ to the left of $i$ .

$- 6 i - 4 (2 \cdot i) - 2 \sqrt[3]{- 64}$

Multiply $2$ by $- 4$ .

$- 6 i - 8 i - 2 \sqrt[3]{- 64}$

Rewrite $- 64$ as ${(- 4)}^{3}$ .

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

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

$- 6 i - 8 i - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$- 6 i - 8 i + 8$

Simplify by adding terms.

Subtract $8 i$ from $- 6 i$ .

$- 14 i + 8$

Reorder $- 14 i$ and $8$ .

$8 - 14 i$