Precalculus Examples

\sqrt[3]{135}

$\sqrt[3]{135}$

Step 1

Rewrite

135

$135$ as

3^{3} \cdot 5

$3^{3} \cdot 5$ .

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Step 1.1

Factor

27

$27$ out of

135

$135$ .

\sqrt[3]{27 (5)}

$\sqrt[3]{27 (5)}$

Step 1.2

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

\sqrt[3]{3^{3} \cdot 5}

$\sqrt[3]{3^{3} \cdot 5}$

\sqrt[3]{3^{3} \cdot 5}

$\sqrt[3]{3^{3} \cdot 5}$

Step 2

Pull terms out from under the radical.

3 \sqrt[3]{5}

$3 \sqrt[3]{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

3 \sqrt[3]{5}

$3 \sqrt[3]{5}$

Decimal Form:

5.12992784 \dots

$5.12992784 \dots$

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

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