Question

simplify \\(\frac{\sqrt{5}}{\sqrt{48}}\\). the simplified expression is \\(\square\\).

Explanation:

Step1: Simplify the denominator

First, we simplify \(\sqrt{48}\). We know that \(48 = 16\times3\), so \(\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}\). So the original expression \(\frac{\sqrt{5}}{\sqrt{48}}\) becomes \(\frac{\sqrt{5}}{4\sqrt{3}}\).

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by \(\sqrt{3}\). So we have:

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Answer:

\(\frac{\sqrt{15}}{12}\)