Question

what is the simplified form of the following expression?

\\(\sqrt3{\frac{4x}{5}}\\)

\\(\circ\\) \\(\frac{\sqrt3{4x}}{5}\\)

\\(\circ\\) \\(\frac{\sqrt3{20x}}{5}\\)

\\(\circ\\) \\(\frac{\sqrt3{100x}}{5}\\)

\\(\circ\\) \\(\frac{\sqrt3{100x}}{125}\\)

Explanation:

Rewrite the radical expression

$$ \sqrt[3]{\frac{4x}{5}} = \frac{\sqrt[3]{4x}}{\sqrt[3]{5}} $$

Rationalize the denominator

$$ \frac{\sqrt[3]{4x}}{\sqrt[3]{5}} \cdot \frac{\sqrt[3]{5^2}}{\sqrt[3]{5^2}} = \frac{\sqrt[3]{4x \cdot 25}}{\sqrt[3]{125}} $$

Simplify the expression

$$ \frac{\sqrt[3]{100x}}{5} $$

Answer:

• (A) \(\frac{\sqrt[3]{4x}}{5}\)
• (B) \(\frac{\sqrt[3]{20x}}{5}\)
• (C) \(\frac{\sqrt[3]{100x}}{5}\) (Correct answer)
• (D) \(\frac{\sqrt[3]{100x}}{125}\)