Simplify cube root of 216-3 cube root of -729+3 square root of -49

$\sqrt[3]{216} - 3 \sqrt[3]{- 729} + 3 \sqrt{- 49}$

Step 1

Simplify each term.

Rewrite $216$ as $6^{3}$ .

$\sqrt[3]{6^{3}} - 3 \sqrt[3]{- 729} + 3 \sqrt{- 49}$

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

$6 - 3 \sqrt[3]{- 729} + 3 \sqrt{- 49}$

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

$6 - 3 \sqrt[3]{{(- 9)}^{3}} + 3 \sqrt{- 49}$

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

$6 - 3 \cdot - 9 + 3 \sqrt{- 49}$

Multiply $- 3$ by $- 9$ .

$6 + 27 + 3 \sqrt{- 49}$

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

$6 + 27 + 3 \sqrt{- 1 (49)}$

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

$6 + 27 + 3 (\sqrt{- 1} \cdot \sqrt{49})$

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

$6 + 27 + 3 (i \cdot \sqrt{49})$

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

$6 + 27 + 3 (i \cdot \sqrt{7^{2}})$

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

$6 + 27 + 3 (i \cdot 7)$

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

$6 + 27 + 3 (7 \cdot i)$

Multiply $7$ by $3$ .

$6 + 27 + 21 i$

Step 2

Add $6$ and $27$ .

$33 + 21 i$