Question

1. \\(\frac{3\sqrt{6}}{2\sqrt{12}}\\)

Explanation:

Step1: Simplify \(\sqrt{12}\)

We know that \(12 = 4\times3\), so \(\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}\).
The expression becomes \(\frac{3\sqrt{6}}{2\times2\sqrt{3}}=\frac{3\sqrt{6}}{4\sqrt{3}}\).

Step2: Rationalize the denominator (or simplify the square roots)

We can use the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) and \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\) (\(a\geq0,b > 0\)).
\(\frac{3\sqrt{6}}{4\sqrt{3}}=\frac{3}{4}\times\sqrt{\frac{6}{3}}=\frac{3}{4}\times\sqrt{2}=\frac{3\sqrt{2}}{4}\)

Answer:

\(\frac{3\sqrt{2}}{4}\)