Basic Math Examples

\sqrt[3]{24} - \sqrt[3]{81}

$\sqrt[3]{24} - \sqrt[3]{81}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

24

$24$ as

2^{3} \cdot 3

$2^{3} \cdot 3$ .

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Step 1.1.1

Factor

8

$8$ out of

24

$24$ .

\sqrt[3]{8 (3)} - \sqrt[3]{81}

$\sqrt[3]{8 (3)} - \sqrt[3]{81}$

Step 1.1.2

Rewrite

8

$8$ as

2^{3}

$2^{3}$ .

\sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{81}

$\sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{81}$

\sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{81}

$\sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{81}$

Step 1.2

Pull terms out from under the radical.

2 \sqrt[3]{3} - \sqrt[3]{81}

$2 \sqrt[3]{3} - \sqrt[3]{81}$

Step 1.3

Rewrite

81

$81$ as

3^{3} \cdot 3

$3^{3} \cdot 3$ .

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Step 1.3.1

Factor

27

$27$ out of

81

$81$ .

2 \sqrt[3]{3} - \sqrt[3]{27 (3)}

$2 \sqrt[3]{3} - \sqrt[3]{27 (3)}$

Step 1.3.2

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

2 \sqrt[3]{3} - \sqrt[3]{3^{3} \cdot 3}

$2 \sqrt[3]{3} - \sqrt[3]{3^{3} \cdot 3}$

2 \sqrt[3]{3} - \sqrt[3]{3^{3} \cdot 3}

$2 \sqrt[3]{3} - \sqrt[3]{3^{3} \cdot 3}$

Step 1.4

Pull terms out from under the radical.

2 \sqrt[3]{3} - (3 \sqrt[3]{3})

$2 \sqrt[3]{3} - (3 \sqrt[3]{3})$

Step 1.5

Multiply

3

$3$ by

- 1

$- 1$ .

2 \sqrt[3]{3} - 3 \sqrt[3]{3}

$2 \sqrt[3]{3} - 3 \sqrt[3]{3}$

2 \sqrt[3]{3} - 3 \sqrt[3]{3}

$2 \sqrt[3]{3} - 3 \sqrt[3]{3}$

Step 2

Subtract

3 \sqrt[3]{3}

$3 \sqrt[3]{3}$ from

2 \sqrt[3]{3}

$2 \sqrt[3]{3}$ .

- \sqrt[3]{3}

$- \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- \sqrt[3]{3}

$- \sqrt[3]{3}$

Decimal Form:

- 1.44224957 \dots

$- 1.44224957 \dots$

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

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