Algebra Examples

$- 2 \sqrt{64} + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

Step 1

Simplify each term.

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Step 1.1

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

$- 2 \sqrt{8^{2}} + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

Step 1.2

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

$- 2 \cdot 8 + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

Step 1.3

Multiply $- 2$ by $8$ .

$- 16 + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

Step 1.4

Rewrite $- 64$ as $- 1 (64)$ .

$- 16 + 5 \sqrt{- 1 (64)} + \sqrt[3]{- 729}$

Step 1.5

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$- 16 + 5 (\sqrt{- 1} \cdot \sqrt{64}) + \sqrt[3]{- 729}$

Step 1.6

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

$- 16 + 5 (i \cdot \sqrt{64}) + \sqrt[3]{- 729}$

Step 1.7

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

$- 16 + 5 (i \cdot \sqrt{8^{2}}) + \sqrt[3]{- 729}$

Step 1.8

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

$- 16 + 5 (i \cdot 8) + \sqrt[3]{- 729}$

Step 1.9

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

$- 16 + 5 (8 \cdot i) + \sqrt[3]{- 729}$

Step 1.10

Multiply $8$ by $5$ .

$- 16 + 40 i + \sqrt[3]{- 729}$

Step 1.11

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

$- 16 + 40 i + \sqrt[3]{{(- 9)}^{3}}$

Step 1.12

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

$- 16 + 40 i - 9$

Step 2

Subtract $9$ from $- 16$ .

$- 25 + 40 i$