The given expression is $\sqrt{\frac{49}{100}}$.

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

$\sqrt{\frac{49}{100}} = \frac{\sqrt{49}}{\sqrt{100}} = \frac{7}{10}$

So, the simplified form of $\sqrt{\frac{49}{100}}$ is $\frac{7}{10}$.

Would you like further details or have any questions?

Here are five related questions you might explore:

1. How do you simplify square roots of other fractions, like $\sqrt{\frac{25}{64}}$?
2. What happens when you simplify a square root with a negative value?
3. Can square roots always be simplified to rational numbers?
4. How do you handle square roots in equations involving variables, such as $\sqrt{\frac{x^2}{y^2}}$?
5. How do you rationalize denominators involving square roots?

Tip: Always simplify square roots by looking for perfect squares in the numerator and denominator.