Basic Math Examples

\sqrt[3]{54} - \sqrt[3]{128}

$\sqrt[3]{54} - \sqrt[3]{128}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

54

$54$ as

3^{3} \cdot 2

$3^{3} \cdot 2$ .

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Step 1.1.1

Factor

27

$27$ out of

54

$54$ .

\sqrt[3]{27 (2)} - \sqrt[3]{128}

$\sqrt[3]{27 (2)} - \sqrt[3]{128}$

Step 1.1.2

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

\sqrt[3]{3^{3} \cdot 2} - \sqrt[3]{128}

$\sqrt[3]{3^{3} \cdot 2} - \sqrt[3]{128}$

\sqrt[3]{3^{3} \cdot 2} - \sqrt[3]{128}

$\sqrt[3]{3^{3} \cdot 2} - \sqrt[3]{128}$

Step 1.2

Pull terms out from under the radical.

3 \sqrt[3]{2} - \sqrt[3]{128}

$3 \sqrt[3]{2} - \sqrt[3]{128}$

Step 1.3

Rewrite

128

$128$ as

4^{3} \cdot 2

$4^{3} \cdot 2$ .

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Step 1.3.1

Factor

64

$64$ out of

128

$128$ .

3 \sqrt[3]{2} - \sqrt[3]{64 (2)}

$3 \sqrt[3]{2} - \sqrt[3]{64 (2)}$

Step 1.3.2

Rewrite

64

$64$ as

4^{3}

$4^{3}$ .

3 \sqrt[3]{2} - \sqrt[3]{4^{3} \cdot 2}

$3 \sqrt[3]{2} - \sqrt[3]{4^{3} \cdot 2}$

3 \sqrt[3]{2} - \sqrt[3]{4^{3} \cdot 2}

$3 \sqrt[3]{2} - \sqrt[3]{4^{3} \cdot 2}$

Step 1.4

Pull terms out from under the radical.

$3 \sqrt[3]{2} - (4 \sqrt[3]{2})$

Step 1.5

Multiply

$4$ by

$- 1$ .

$3 \sqrt[3]{2} - 4 \sqrt[3]{2}$

$3 \sqrt[3]{2} - 4 \sqrt[3]{2}$

Step 2

Subtract

$4 \sqrt[3]{2}$ from

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

$- \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \sqrt[3]{2}$

Decimal Form:

$- 1.25992104 \dots$

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