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Simplify 6 cube root of 27p^2-3 cube root of 125p^2

$6 \sqrt[3]{27 p^{2}} - 3 \sqrt[3]{125 p^{2}}$

Step 1

Simplify each term.

Rewrite

$27$ as

$3^{3}$ .

$6 \sqrt[3]{3^{3} p^{2}} - 3 \sqrt[3]{125 p^{2}}$

Pull terms out from under the radical.

$6 (3 \sqrt[3]{p^{2}}) - 3 \sqrt[3]{125 p^{2}}$

Multiply

$3$ by

$6$ .

$18 \sqrt[3]{p^{2}} - 3 \sqrt[3]{125 p^{2}}$

Rewrite

$125$ as

$5^{3}$ .

$18 \sqrt[3]{p^{2}} - 3 \sqrt[3]{5^{3} p^{2}}$

Pull terms out from under the radical.

$18 \sqrt[3]{p^{2}} - 3 (5 \sqrt[3]{p^{2}})$

Multiply

$5$ by

$- 3$ .

$18 \sqrt[3]{p^{2}} - 15 \sqrt[3]{p^{2}}$

$18 \sqrt[3]{p^{2}} - 15 \sqrt[3]{p^{2}}$

Step 2

Subtract

$15 \sqrt[3]{p^{2}}$ from

$18 \sqrt[3]{p^{2}}$ .

$3 \sqrt[3]{p^{2}}$

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