Question

rationalize the denominator.

\\\frac{\sqrt{2}}{\sqrt{5}}\\

\\\frac{\sqrt{2}}{\sqrt{5}} = \square \text{ (simplify your answer.)}\\

Explanation:

⚡ Using what you learned: Rationalizing Denominators

Step 1: Multiply numerator and denominator by \(\sqrt{5}\)

$$ \frac{\sqrt{2}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} $$

Step 2: Simplify the expression

$$ \frac{\sqrt{2 \cdot 5}}{\sqrt{5 \cdot 5}} = \frac{\sqrt{10}}{5} $$

Answer:

$$ \frac{\sqrt{10}}{5} $$