Algebra Examples

$- 5 \sqrt[3]{- 64} + \sqrt[3]{- 1} - \sqrt{- 25}$

Step 1

Simplify each term.

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Step 1.1

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

$- 5 \sqrt[3]{{(- 4)}^{3}} + \sqrt[3]{- 1} - \sqrt{- 25}$

Step 1.2

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

$- 5 \cdot - 4 + \sqrt[3]{- 1} - \sqrt{- 25}$

Step 1.3

Multiply $- 5$ by $- 4$ .

$20 + \sqrt[3]{- 1} - \sqrt{- 25}$

Step 1.4

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$20 + \sqrt[3]{{(- 1)}^{3}} - \sqrt{- 25}$

Step 1.5

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

$20 - 1 - \sqrt{- 25}$

Step 1.6

Rewrite $- 25$ as $- 1 (25)$ .

$20 - 1 - \sqrt{- 1 (25)}$

Step 1.7

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$20 - 1 - (\sqrt{- 1} \cdot \sqrt{25})$

Step 1.8

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

$20 - 1 - (i \cdot \sqrt{25})$

Step 1.9

Rewrite $25$ as $5^{2}$ .

$20 - 1 - (i \cdot \sqrt{5^{2}})$

Step 1.10

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

$20 - 1 - (i \cdot 5)$

Step 1.11

Move $5$ to the left of $i$ .

$20 - 1 - (5 \cdot i)$

Step 1.12

Multiply $5$ by $- 1$ .

$20 - 1 - 5 i$

Step 2

Subtract $1$ from $20$ .

$19 - 5 i$