Finite Math Examples

$a^{3} + 2^{3} = 4^{3}$

Step 1

Raise $2$ to the power of $3$ .

$a^{3} + 8 = 4^{3}$

Step 2

Raise $4$ to the power of $3$ .

$a^{3} + 8 = 64$

Step 3

Move all terms not containing $a$ to the right side of the equation.

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Step 3.1

Subtract $8$ from both sides of the equation.

$a^{3} = 64 - 8$

Step 3.2

Subtract $8$ from $64$ .

$a^{3} = 56$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \sqrt[3]{56}$

Step 5

Simplify $\sqrt[3]{56}$ .

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Step 5.1

Rewrite $56$ as $2^{3} \cdot 7$ .

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Step 5.1.1

Factor $8$ out of $56$ .

$a = \sqrt[3]{8 (7)}$

Step 5.1.2

Rewrite $8$ as $2^{3}$ .

$a = \sqrt[3]{2^{3} \cdot 7}$

Step 5.2

Pull terms out from under the radical.

$a = 2 \sqrt[3]{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = 2 \sqrt[3]{7}$

Decimal Form:

$a = 3.82586236 \dots$