https://file.aiquickdraw.com/mathbot/file/1730126404634wugtfoah.jpg

The expression in the image shows:

\[
\frac{3}{\sqrt{75}}
\]

We can simplify this as follows:

1. **Simplify the square root**:
   \[
   \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}
   \]

   So the expression becomes:
   \[
   \frac{3}{5\sqrt{3}}
   \]

2. **Rationalize the denominator** by multiplying the numerator and denominator by \(\sqrt{3}\):
   \[
   \frac{3}{5\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{5 \times 3} = \frac{\sqrt{3}}{5}
   \]

Therefore, the simplified form of \(\frac{3}{\sqrt{75}}\) is \(\boxed{\frac{\sqrt{3}}{5}}\).

Would you like more details or have any questions about this solution? 

Here are 5 related questions:
1. How can we simplify other similar expressions with square roots in the denominator?
2. What is the general method for rationalizing a denominator?
3. How do we handle square roots of larger composite numbers?
4. What is the importance of expressing results with rationalized denominators?
5. How can we apply similar steps to simplify expressions involving cube roots?

**Tip:** Whenever you encounter a square root in the denominator, the goal is to eliminate it by multiplying both numerator and denominator by that square root. This is called rationalizing the denominator.

Simplify the expression \( \frac{3}{\sqrt{75}} \).

Learn how to simplify the expression \( \frac{3}{\sqrt{75}} \) by rationalizing the denominator. This solution breaks down each step in simplifying square roots and rationalizing fractions, ideal for Grades 8-10.

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