The expression you provided is:

\[
\sqrt{\dfrac{36}{169}} 
\]

To solve this:

1. Take the square root of the numerator (36) and the square root of the denominator (169) separately.

\[
\sqrt{36} = 6 \quad \text{and} \quad \sqrt{169} = 13
\]

2. Therefore:

\[
\sqrt{\dfrac{36}{169}} = \dfrac{6}{13}
\]

The final answer is:

\[
\dfrac{6}{13}
\]

Would you like further details or have any questions?

Here are some related questions to explore:

1. What is the square root of other fractions, such as \(\sqrt{\dfrac{49}{81}}\)?
2. How do you simplify square roots of non-perfect squares?
3. What are the properties of square roots of negative numbers (complex numbers)?
4. How do square roots relate to exponents?
5. How would you solve \(\sqrt{\dfrac{25}{100}}\)?

**Tip:** When simplifying square roots of fractions, always simplify the square root of the numerator and denominator separately if possible!

Learn how to simplify the square root of the fraction 36/169. This problem covers key algebraic concepts, including the simplification of radicals and fractions, making it suitable for students in Grades 6-8.

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