Simplify cube root of 375x- cube root of 3x^4

$\sqrt[3]{375 x} - \sqrt[3]{3 x^{4}}$

Step 1

Rewrite $375 x$ as $5^{3} \cdot (3 x)$ .

Factor $125$ out of $375$ .

$\sqrt[3]{125 (3) x} - \sqrt[3]{3 x^{4}}$

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 3 x} - \sqrt[3]{3 x^{4}}$

Add parentheses.

$\sqrt[3]{5^{3} \cdot (3 x)} - \sqrt[3]{3 x^{4}}$

$\sqrt[3]{5^{3} \cdot (3 x)} - \sqrt[3]{3 x^{4}}$

Step 2

Pull terms out from under the radical.

$5 \sqrt[3]{3 x} - \sqrt[3]{3 x^{4}}$

Step 3

Rewrite $3 x^{4}$ as $x^{3} \cdot (3 x)$ .

Factor out $x^{3}$ .

$5 \sqrt[3]{3 x} - \sqrt[3]{3 (x^{3} x)}$

Reorder $3$ and $x^{3}$ .

$5 \sqrt[3]{3 x} - \sqrt[3]{x^{3} \cdot 3 x}$

Add parentheses.

$5 \sqrt[3]{3 x} - \sqrt[3]{x^{3} \cdot (3 x)}$

$5 \sqrt[3]{3 x} - \sqrt[3]{x^{3} \cdot (3 x)}$

Step 4

Pull terms out from under the radical.

$5 \sqrt[3]{3 x} - x \sqrt[3]{3 x}$

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