To rationalize the denominator of the expression $\frac{1}{\sqrt{3}}$, we can achieve this by multiplying both the numerator and the denominator by $\sqrt{3}$.

When dealing with a fraction such as $\frac{1}{\sqrt{3}}$, the objective of rationalizing the denominator is to remove the square root from the denominator. This is accomplished by multiplying both the numerator and the denominator by the square root present in the denominator—in this case, $\sqrt{3}$.

Let’s break down the steps involved in this process:

1. Begin with the fraction $\frac{1}{\sqrt{3}}$.
2. Multiply both the numerator and the denominator by $\sqrt{3}$. This results in the expression $\frac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}$.
3. Simplify the resulting expression. The numerator simplifies to $\sqrt{3}$, while the denominator simplifies as follows: $\sqrt{3} \cdot \sqrt{3} = 3.$

Consequently, we find that $\frac{1}{\sqrt{3}}$ can be rewritten as $\frac{\sqrt{3}}{3}$. Now, the denominator is rationalized, as it no longer contains a square root. This technique is particularly useful because it often simplifies subsequent calculations and is a standard practice in mathematics.