To simplify the expression \( \frac{3}{\sqrt{27}} \times \sqrt{75} \), follow these steps:

1. **Simplify \( \sqrt{27} \)**:
   \[
   \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
   \]

2. **Simplify \( \sqrt{75} \)**:
   \[
   \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
   \]

3. **Substitute back into the expression**:
   \[
   \frac{3}{\sqrt{27}} \times \sqrt{75} = \frac{3}{3\sqrt{3}} \times 5\sqrt{3}
   \]

4. **Simplify**:
   \[
   = \frac{3 \times 5\sqrt{3}}{3\sqrt{3}} = \frac{15\sqrt{3}}{3\sqrt{3}} = 5
   \]

Thus, the simplified result is:
\[
\boxed{5}
\]

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you simplify other radical expressions?
2. Can you explain the properties of square roots?
3. What are some common methods for multiplying radicals?
4. How do you handle more complex fractions involving radicals?
5. What is the significance of rationalizing the denominator? 

**Tip**: Always look for perfect squares inside square roots to simplify expressions efficiently.

Explore how to simplify the radical expression 3/√27 * √75 through a step-by-step approach, covering essential concepts like simplifying square roots and rationalizing the denominator. This guide provides insight into the multiplication of radicals and is suitable for Grades 8-10.

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