Simplify the Radical Expression 3 cube root of 81-2 cube root of 54

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

Step 1

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

Factor $27$ out of $81$ .

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

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 $3^{3} \cdot 2$ .

Factor $27$ out of $54$ .

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

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:

$5.42071983 \dots$

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