The expression you are asked to simplify is:

$\sqrt{\frac{9}{64}}$

We can simplify this by taking the square root of both the numerator and the denominator separately:

$\sqrt{\frac{9}{64}} = \frac{\sqrt{9}}{\sqrt{64}} = \frac{3}{8}$

Thus, the correct answer is:

$\boxed{\frac{3}{8}}$

This corresponds to option e in the list.

Would you like further details on how this simplification works, or do you have any other questions?

Here are 5 related questions to explore further:

1. What is the square root of a fraction and how does it work in general?
2. How do you simplify expressions involving square roots of numbers that are not perfect squares?
3. Can you find the square root of larger fractions using this method?
4. How can you use the property of radicals to simplify more complex square root expressions?
5. What is the importance of simplifying fractions before finding their square roots?

Tip: Always break down a fraction's square root by applying the square root separately to both the numerator and the denominator.