Algebra Examples

$3 \sqrt[3]{81} - 2 \sqrt[3]{54}$

Step 1

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 1.1

Factor $27$ out of $81$ .

$3 \sqrt[3]{27 (3)} - 2 \sqrt[3]{54}$

Step 1.2

Rewrite $27$ as $3^{3}$ .

$3 \sqrt[3]{3^{3} \cdot 3} - 2 \sqrt[3]{54}$

$3 \sqrt[3]{3^{3} \cdot 3} - 2 \sqrt[3]{54}$

Step 2

Pull terms out from under the radical.

$3 (3 \sqrt[3]{3}) - 2 \sqrt[3]{54}$

Step 3

Multiply $3$ by $3$ .

$9 \sqrt[3]{3} - 2 \sqrt[3]{54}$

Step 4

Rewrite $54$ as $3^{3} \cdot 2$ .

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Step 4.1

Factor $27$ out of $54$ .

$9 \sqrt[3]{3} - 2 \sqrt[3]{27 (2)}$

Step 4.2

Rewrite $27$ as $3^{3}$ .

$9 \sqrt[3]{3} - 2 \sqrt[3]{3^{3} \cdot 2}$

$9 \sqrt[3]{3} - 2 \sqrt[3]{3^{3} \cdot 2}$

Step 5

Pull terms out from under the radical.

$9 \sqrt[3]{3} - 2 (3 \sqrt[3]{2})$

Step 6

Multiply $3$ by $- 2$ .

$9 \sqrt[3]{3} - 6 \sqrt[3]{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt[3]{3} - 6 \sqrt[3]{2}$

Decimal Form:

$5.42071983 \dots$

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