Question

rationalize the denominator. assume

\\\frac{6}{\sqrt3{5}}\\

\\\frac{6}{\sqrt3{5}} = \square\\

(simplify your answer. type an exact answer us

Explanation:

⚡ Using what you learned: Rationalizing Denominators

Step 1: Identify the multiplier

To eliminate the cube root in the denominator, multiply the numerator and the denominator by a factor that completes a perfect cube under the radical:

$$ \sqrt[3]{5} \cdot \sqrt[3]{5^2} = \sqrt[3]{5^3} = 5 $$

Therefore, the multiplier is \(\sqrt[3]{25}\).

Step 2: Multiply numerator and denominator

$$ \frac{6}{\sqrt[3]{5}} \cdot \frac{\sqrt[3]{25}}{\sqrt[3]{25}} = \frac{6\sqrt[3]{25}}{\sqrt[3]{125}} $$

Step 3: Simplify the expression

$$ \frac{6\sqrt[3]{25}}{5} $$

Answer:

$$ \frac{6\sqrt[3]{25}}{5} $$