To simplify \( \frac{20}{\sqrt{75}} \), follow these steps:

1. **Simplify the square root**:
   - First, factor 75: \( 75 = 25 \times 3 \).
   - Therefore, \( \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3} \).

2. **Rewrite the expression**:
   - Now the expression becomes \( \frac{20}{5\sqrt{3}} \).

3. **Simplify the fraction**:
   - \( \frac{20}{5} = 4 \), so we get \( \frac{4}{\sqrt{3}} \).

4. **Rationalize the denominator**:
   - To eliminate the square root from the denominator, multiply both the numerator and denominator by \( \sqrt{3} \):
   \[
   \frac{4}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{3}.
   \]

Thus, \( \frac{20}{\sqrt{75}} = \frac{4\sqrt{3}}{3} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you rationalize a denominator?
2. How would you simplify \( \frac{15}{\sqrt{50}} \)?
3. What are the properties of square roots?
4. Can you simplify \( \frac{30}{\sqrt{45}} \)?
5. How does factoring help simplify radicals?

**Tip:** Always look to factor perfect squares when simplifying square roots.

Simplify the expression 20/√75 with this step-by-step guide. Learn key concepts such as simplifying radicals and rationalizing denominators, using the formulas √(a × b) = √a × √b and rationalization. Suitable for Grades 8-10 students looking to strengthen their algebraic skills.

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