Pre-Algebra Examples

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

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

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

$1 \cdot - 1 = - 1$

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

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

Step 2

Simplify each term.

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Step 2.1

Rewrite

256

$256$ as

4^{4}

$4^{4}$ .

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

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

Step 2.2

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

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

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

Step 2.3

Multiply

3

$3$ by

4

$4$ .

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

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

Step 2.4

Rewrite

64

$64$ as

4^{3}

$4^{3}$ .

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

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

Step 2.5

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

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

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

Step 2.6

Multiply

- 1

$- 1$ by

4

$4$ .

12 - 4 + \sqrt{169}

$12 - 4 + \sqrt{169}$

Step 2.7

Rewrite

169

$169$ as

13^{2}

$13^{2}$ .

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

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

Step 2.8

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

12 - 4 + 13

$12 - 4 + 13$

12 - 4 + 13

$12 - 4 + 13$

Step 3

Simplify by adding and subtracting.

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Step 3.1

Subtract

4

$4$ from

12

$12$ .

8 + 13

$8 + 13$

Step 3.2

Add

8

$8$ and

13

$13$ .

21

$21$

21

$21$