Question

1. \\(\frac{5\sqrt{15}}{4\sqrt{3}}\\)

Explanation:

Step1: Simplify the square roots

We know that $\sqrt{15}=\sqrt{3\times5}=\sqrt{3}\times\sqrt{5}$. So we can rewrite the numerator:
$\frac{5\sqrt{15}}{4\sqrt{3}}=\frac{5\times\sqrt{3}\times\sqrt{5}}{4\sqrt{3}}$

Step2: Cancel out common terms

The $\sqrt{3}$ in the numerator and the $\sqrt{3}$ in the denominator can be canceled out (since $\frac{\sqrt{3}}{\sqrt{3}} = 1$ for $\sqrt{3}
eq0$). So we have:
$\frac{5\times\sqrt{5}}{4}=\frac{5\sqrt{5}}{4}$

Answer:

$\frac{5\sqrt{5}}{4}$