Question

1. \\(\frac{3\sqrt{15}}{4\sqrt{48}}\\)

Explanation:

Step1: Simplify $\sqrt{48}$

Factor 48: $48 = 16\times3$, so $\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}$

Step2: Substitute back into the fraction

The fraction becomes $\frac{3\sqrt{15}}{4\times4\sqrt{3}}=\frac{3\sqrt{15}}{16\sqrt{3}}$

Step3: Rationalize the denominator (divide $\sqrt{15}$ and $\sqrt{3}$)

$\sqrt{15}\div\sqrt{3}=\sqrt{\frac{15}{3}}=\sqrt{5}$

Step4: Simplify the fraction

Now we have $\frac{3\sqrt{5}}{16}$

Answer:

$\frac{3\sqrt{5}}{16}$