Algebra Examples

$- 5 \sqrt[3]{64} + 3 \sqrt{25} + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $64$ as $4^{3}$ .

$- 5 \sqrt[3]{4^{3}} + 3 \sqrt{25} + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1.2

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

$- 5 \cdot 4 + 3 \sqrt{25} + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1.3

Multiply $- 5$ by $4$ .

$- 20 + 3 \sqrt{25} + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1.4

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

$- 20 + 3 \sqrt{5^{2}} + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1.5

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

$- 20 + 3 \cdot 5 + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1.6

Multiply $3$ by $5$ .

$- 20 + 15 + 2 \sqrt[3]{512} - 3 \sqrt[3]{- 64}$

Step 1.7

Rewrite $512$ as $8^{3}$ .

$- 20 + 15 + 2 \sqrt[3]{8^{3}} - 3 \sqrt[3]{- 64}$

Step 1.8

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

$- 20 + 15 + 2 \cdot 8 - 3 \sqrt[3]{- 64}$

Step 1.9

Multiply $2$ by $8$ .

$- 20 + 15 + 16 - 3 \sqrt[3]{- 64}$

Step 1.10

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

$- 20 + 15 + 16 - 3 \sqrt[3]{{(- 4)}^{3}}$

Step 1.11

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

$- 20 + 15 + 16 - 3 \cdot - 4$

Step 1.12

Multiply $- 3$ by $- 4$ .

$- 20 + 15 + 16 + 12$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $- 20$ and $15$ .

$- 5 + 16 + 12$

Step 2.2

Add $- 5$ and $16$ .

$11 + 12$

Step 2.3

Add $11$ and $12$ .

$23$