Pre-Algebra Examples

$3 \sqrt[4]{256} + - \sqrt[3]{64} + \sqrt{169}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$3 \sqrt[4]{256} - \sqrt[3]{64} + \sqrt{169}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $256$ as $4^{4}$ .

$3 \sqrt[4]{4^{4}} - \sqrt[3]{64} + \sqrt{169}$

Step 2.2

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

$3 \cdot 4 - \sqrt[3]{64} + \sqrt{169}$

Step 2.3

Multiply $3$ by $4$ .

$12 - \sqrt[3]{64} + \sqrt{169}$

Step 2.4

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

$12 - \sqrt[3]{4^{3}} + \sqrt{169}$

Step 2.5

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

$12 - 1 \cdot 4 + \sqrt{169}$

Step 2.6

Multiply $- 1$ by $4$ .

$12 - 4 + \sqrt{169}$

Step 2.7

Rewrite $169$ as $13^{2}$ .

$12 - 4 + \sqrt{13^{2}}$

Step 2.8

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

$12 - 4 + 13$

Step 3

Simplify by adding and subtracting.

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Step 3.1

Subtract $4$ from $12$ .

$8 + 13$

Step 3.2

Add $8$ and $13$ .

$21$