Question

express in simplest form with a rational denominator.
\\(\dfrac{5}{\sqrt{3}}\\)

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{3}$ to rationalize the denominator.

To rationalize the denominator of a fraction with a square root in the denominator, we multiply the numerator and the denominator by the same square root. So we have $\frac{5}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$.

Step2: Simplify the numerator and the denominator.

The numerator becomes $5\times\sqrt{3} = 5\sqrt{3}$, and the denominator becomes $\sqrt{3}\times\sqrt{3} = 3$ (since $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$). So the fraction simplifies to $\frac{5\sqrt{3}}{3}$.

Answer:

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