Precalculus Examples

\sqrt[3]{54 x^{17}}

$\sqrt[3]{54 x^{17}}$

Step 1

Rewrite

54 x^{17}

$54 x^{17}$ as

{(3 x^{5})}^{3} \cdot (2 x^{2})

${(3 x^{5})}^{3} \cdot (2 x^{2})$ .

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Step 1.1

Factor

27

$27$ out of

54

$54$ .

\sqrt[3]{27 (2) x^{17}}

$\sqrt[3]{27 (2) x^{17}}$

Step 1.2

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

\sqrt[3]{3^{3} \cdot 2 x^{17}}

$\sqrt[3]{3^{3} \cdot 2 x^{17}}$

Step 1.3

Factor out

x^{15}

$x^{15}$ .

\sqrt[3]{3^{3} \cdot 2 (x^{15} x^{2})}

$\sqrt[3]{3^{3} \cdot 2 (x^{15} x^{2})}$

Step 1.4

Rewrite

x^{15}

$x^{15}$ as

{(x^{5})}^{3}

${(x^{5})}^{3}$ .

\sqrt[3]{3^{3} \cdot 2 ({(x^{5})}^{3} x^{2})}

$\sqrt[3]{3^{3} \cdot 2 ({(x^{5})}^{3} x^{2})}$

Step 1.5

Move

2

$2$ .

\sqrt[3]{3^{3} {(x^{5})}^{3} \cdot 2 x^{2}}

$\sqrt[3]{3^{3} {(x^{5})}^{3} \cdot 2 x^{2}}$

Step 1.6

Rewrite

3^{3} {(x^{5})}^{3}

$3^{3} {(x^{5})}^{3}$ as

{(3 x^{5})}^{3}

${(3 x^{5})}^{3}$ .

\sqrt[3]{{(3 x^{5})}^{3} \cdot 2 x^{2}}

$\sqrt[3]{{(3 x^{5})}^{3} \cdot 2 x^{2}}$

Step 1.7

Add parentheses.

\sqrt[3]{{(3 x^{5})}^{3} \cdot (2 x^{2})}

$\sqrt[3]{{(3 x^{5})}^{3} \cdot (2 x^{2})}$

\sqrt[3]{{(3 x^{5})}^{3} \cdot (2 x^{2})}

$\sqrt[3]{{(3 x^{5})}^{3} \cdot (2 x^{2})}$

Step 2

Pull terms out from under the radical.

3 x^{5} \sqrt[3]{2 x^{2}}

$3 x^{5} \sqrt[3]{2 x^{2}}$

Enter a problem...

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

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