Pre-Algebra Examples

$\frac{39}{2 \sqrt[3]{5} - 1}$

Step 1

Multiply $\frac{39}{2 \sqrt[3]{5} - 1}$ by $\frac{{(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}}{{(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}}$ .

$\frac{39}{2 \sqrt[3]{5} - 1} \cdot \frac{{(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}}{{(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}}$

Step 2

Multiply $\frac{39}{2 \sqrt[3]{5} - 1}$ by $\frac{{(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}}{{(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}}$ .

$\frac{39 ({(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2})}{(2 \sqrt[3]{5} - 1) ({(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{39 ({(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2})}{2 \sqrt[3]{5} {(2 \sqrt[3]{5})}^{2} + 4 {\sqrt[3]{5}}^{2} + 2 \sqrt[3]{5} {(- 1)}^{2} - {(2 \sqrt[3]{5})}^{2} - 2 \sqrt[3]{5} + {(- 1)}^{3}}$

Step 4

Simplify.

$\frac{39 ({(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2})}{39}$

Step 5

Cancel the common factor of $39$ .

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Step 5.1

Cancel the common factor.

$\frac{39 ({(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2})}{39}$

Step 5.2

Divide ${(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}$ by $1$ .

${(2 \sqrt[3]{5})}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}$

Step 6

Simplify each term.

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Step 6.1

Apply the product rule to $2 \sqrt[3]{5}$ .

$2^{2} {\sqrt[3]{5}}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}$

Step 6.2

Raise $2$ to the power of $2$ .

$4 {\sqrt[3]{5}}^{2} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}$

Step 6.3

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$4 \sqrt[3]{5^{2}} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}$

Step 6.4

Raise $5$ to the power of $2$ .

$4 \sqrt[3]{25} - (2 \sqrt[3]{5}) \cdot - 1 + {(- 1)}^{2}$

Step 6.5

Multiply $2$ by $- 1$ .

$4 \sqrt[3]{25} - 2 \sqrt[3]{5} \cdot - 1 + {(- 1)}^{2}$

Step 6.6

Multiply $- 1$ by $- 2$ .

$4 \sqrt[3]{25} + 2 \sqrt[3]{5} + {(- 1)}^{2}$

Step 6.7

Raise $- 1$ to the power of $2$ .

$4 \sqrt[3]{25} + 2 \sqrt[3]{5} + 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt[3]{25} + 2 \sqrt[3]{5} + 1$

Decimal Form:

$16.11602284 \dots$