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We are tasked with finding a value for \( a \) such that \( \sqrt{a} \) is a rational number but not an integer.

Let's go through the options one by one:

1. **0**:  
   \( \sqrt{0} = 0 \), which is an integer. So, this option is **not valid** because we are looking for a value where the square root is not an integer.

2. **16**:  
   \( \sqrt{16} = 4 \), which is also an integer. Hence, this option is **not valid** either.

3. **-5**:  
   The square root of a negative number is not a real number, so \( \sqrt{-5} \) is not rational. Therefore, this option is also **not valid**.

4. **4/9**:  
   \( \sqrt{\frac{4}{9}} = \frac{2}{3} \), which is a rational number but not an integer. This option **is valid**.

### Conclusion: 
The only valid option is **4/9**, because its square root is a rational number and not an integer.

Would you like any further details or clarification?

Here are 5 follow-up questions you might find helpful:
1. What defines a rational number?
2. What is the difference between a rational number and an integer?
3. Why can't a negative number have a real square root?
4. What happens when you take the square root of fractions?
5. Can you have other values for \( a \) where \( \sqrt{a} \) is a rational number but not an integer?

**Tip**: For fractions, taking the square root involves taking the square root of both the numerator and the denominator separately.

Provide a value for a so that √a is a Rational Number but NOT an Integer.

Explore the solution to the problem of finding a value for 'a' such that the square root of 'a' is a rational number but not an integer. Learn about rational numbers, square roots, and how to distinguish between integers and rational numbers. Suitable for students in Grades 8-10.

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