Simplify -3 square root of -49+ cube root of -729+ square root of -4-3 cube root of -64

$- 3 \sqrt{- 49} + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

Step 1

Simplify each term.

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

$- 3 \sqrt{- 1 (49)} + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 3 (\sqrt{- 1} \cdot \sqrt{49}) + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 3 (i \cdot \sqrt{49}) + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 3 (i \cdot \sqrt{7^{2}}) + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 3 (i \cdot 7) + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 3 (7 \cdot i) + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

Multiply $7$ by $- 3$ .

$- 21 i + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

Rewrite $- 729$ as ${(- 9)}^{3}$ .

$- 21 i + \sqrt[3]{{(- 9)}^{3}} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + \sqrt{- 4} - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + \sqrt{- 1 (4)} - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + \sqrt{- 1} \cdot \sqrt{4} - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + i \cdot \sqrt{4} - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + i \cdot \sqrt{2^{2}} - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + i \cdot 2 - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + 2 \cdot i - 3 \sqrt[3]{- 64}$

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

$- 21 i - 9 + 2 i - 3 \sqrt[3]{{(- 4)}^{3}}$

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

$- 21 i - 9 + 2 i - 3 \cdot - 4$

Multiply $- 3$ by $- 4$ .

$- 21 i - 9 + 2 i + 12$

Step 2

Simplify by adding terms.

Add $- 21 i$ and $2 i$ .

$- 9 - 19 i + 12$

Add $- 9$ and $12$ .

$3 - 19 i$