Question

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

Explanation:

Step1: Simplify the square root in the denominator

We know that $\sqrt{12}=\sqrt{4\times3}$. Using the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 4$ and $b=3$ and $a\geq0,b\geq0$), we get $\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}$. So the expression becomes $\frac{3}{2\sqrt{3}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{3}$. So we have $\frac{3\times\sqrt{3}}{2\sqrt{3}\times\sqrt{3}}$.

Step3: Simplify the numerator and the denominator

The numerator is $3\sqrt{3}$ and the denominator is $2\times(\sqrt{3})^2 = 2\times3=6$. So the fraction becomes $\frac{3\sqrt{3}}{6}$.

Step4: Reduce the fraction

We can divide both the numerator and the denominator by 3. So $\frac{3\sqrt{3}\div3}{6\div3}=\frac{\sqrt{3}}{2}$.

Answer:

$\frac{\sqrt{3}}{2}$