To simplify the expression $\frac{1}{\sqrt{6}}$, we need to eliminate the square root from the denominator. This process is called "rationalizing the denominator."

Step-by-Step Solution

1. Multiply by the Conjugate: We multiply both the numerator and the denominator by $\sqrt{6}$ to remove the square root from the denominator:

   $\frac{1}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{\sqrt{6}}{6}$

2. Simplified Form: The simplest form of $\frac{1}{\sqrt{6}}$ is $\frac{\sqrt{6}}{6}$.

Correct Answer

The correct choice is a. $\frac{\sqrt{6}}{6}$.

Would you like further details on this explanation or have any other questions?

Here are some related questions you might find interesting:

1. How do you simplify expressions with square roots in the numerator?
2. What does it mean to "rationalize the denominator"?
3. How do you simplify an expression involving higher roots (like cube roots)?
4. What are some common mistakes when simplifying radical expressions?
5. How does this process change for expressions with complex numbers?

Tip: When simplifying expressions, always look for ways to make the denominator rational by removing any roots or irrational numbers.