Simplify 3 cube root of 27r-3 cube root of 8r

$3 \sqrt[3]{27 r} - 3 \sqrt[3]{8 r}$

Step 1

Simplify each term.

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

$3 \sqrt[3]{3^{3} r} - 3 \sqrt[3]{8 r}$

Pull terms out from under the radical.

$3 (3 \sqrt[3]{r}) - 3 \sqrt[3]{8 r}$

Multiply $3$ by $3$ .

$9 \sqrt[3]{r} - 3 \sqrt[3]{8 r}$

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

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

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

Step 2

Subtract $6 \sqrt[3]{r}$ from $9 \sqrt[3]{r}$ .

$3 \sqrt[3]{r}$

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