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To simplify the expression \(\sqrt{\frac{36}{49}}\):

We can break it down into two parts:

\[
\sqrt{\frac{36}{49}} = \frac{\sqrt{36}}{\sqrt{49}}.
\]

- \(\sqrt{36} = 6\) (since \(6^2 = 36\))
- \(\sqrt{49} = 7\) (since \(7^2 = 49\))

Therefore,

\[
\sqrt{\frac{36}{49}} = \frac{6}{7}.
\]

The simplified form is \(\frac{6}{7}\).

Would you like more details, or have any other questions?

Here are five related questions to practice:
1. Simplify \(\sqrt{\frac{25}{64}}\).
2. Simplify \(\sqrt{\frac{9}{16}}\).
3. What is \(\sqrt{81}\)?
4. Simplify \(\sqrt{\frac{144}{169}}\).
5. Simplify \(\sqrt{100}\).

**Tip:** When simplifying square roots of fractions, remember that you can apply the square root to the numerator and denominator separately.

Learn how to simplify square roots of fractions with this example: \(\sqrt{\frac{36}{49}} = \frac{6}{7}\). This tutorial covers the process of applying square roots to both the numerator and the denominator separately. Suitable for students in Grades 6-8.

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