Basic Math Examples

3 \sqrt[3]{192} + 3 \sqrt[3]{24}

$3 \sqrt[3]{192} + 3 \sqrt[3]{24}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

192

$192$ as

4^{3} \cdot 3

$4^{3} \cdot 3$ .

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Step 1.1.1

Factor

64

$64$ out of

192

$192$ .

3 \sqrt[3]{64 (3)} + 3 \sqrt[3]{24}

$3 \sqrt[3]{64 (3)} + 3 \sqrt[3]{24}$

Step 1.1.2

Rewrite

64

$64$ as

4^{3}

$4^{3}$ .

3 \sqrt[3]{4^{3} \cdot 3} + 3 \sqrt[3]{24}

$3 \sqrt[3]{4^{3} \cdot 3} + 3 \sqrt[3]{24}$

3 \sqrt[3]{4^{3} \cdot 3} + 3 \sqrt[3]{24}

$3 \sqrt[3]{4^{3} \cdot 3} + 3 \sqrt[3]{24}$

Step 1.2

Pull terms out from under the radical.

3 (4 \sqrt[3]{3}) + 3 \sqrt[3]{24}

$3 (4 \sqrt[3]{3}) + 3 \sqrt[3]{24}$

Step 1.3

Multiply

4

$4$ by

3

$3$ .

12 \sqrt[3]{3} + 3 \sqrt[3]{24}

$12 \sqrt[3]{3} + 3 \sqrt[3]{24}$

Step 1.4

Rewrite

24

$24$ as

2^{3} \cdot 3

$2^{3} \cdot 3$ .

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Step 1.4.1

Factor

8

$8$ out of

24

$24$ .

12 \sqrt[3]{3} + 3 \sqrt[3]{8 (3)}

$12 \sqrt[3]{3} + 3 \sqrt[3]{8 (3)}$

Step 1.4.2

Rewrite

8

$8$ as

2^{3}

$2^{3}$ .

12 \sqrt[3]{3} + 3 \sqrt[3]{2^{3} \cdot 3}

$12 \sqrt[3]{3} + 3 \sqrt[3]{2^{3} \cdot 3}$

12 \sqrt[3]{3} + 3 \sqrt[3]{2^{3} \cdot 3}

$12 \sqrt[3]{3} + 3 \sqrt[3]{2^{3} \cdot 3}$

Step 1.5

Pull terms out from under the radical.

12 \sqrt[3]{3} + 3 (2 \sqrt[3]{3})

$12 \sqrt[3]{3} + 3 (2 \sqrt[3]{3})$

Step 1.6

Multiply

2

$2$ by

3

$3$ .

12 \sqrt[3]{3} + 6 \sqrt[3]{3}

$12 \sqrt[3]{3} + 6 \sqrt[3]{3}$

12 \sqrt[3]{3} + 6 \sqrt[3]{3}

$12 \sqrt[3]{3} + 6 \sqrt[3]{3}$

Step 2

Add

12 \sqrt[3]{3}

$12 \sqrt[3]{3}$ and

6 \sqrt[3]{3}

$6 \sqrt[3]{3}$ .

18 \sqrt[3]{3}

$18 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

18 \sqrt[3]{3}

$18 \sqrt[3]{3}$

Decimal Form:

25.96049226 \dots

$25.96049226 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$