Indicate whether each real number is rational or irrational.

Rational

Irrational

−196⎯⎯⎯⎯⎯⎯√−196

137299137299

15⎯⎯⎯⎯√3153

3π3π

Let's classify each number as rational or irrational:

1. **−196**: Rational. It can be expressed as \(-196/1\).

2. **\(\sqrt{-196}\)**: Irrational. This is an imaginary number (\(14i\)), which is not a real number.

3. **137299137299**: Rational. This is a whole number, so it can be expressed as \(137299137299/1\).

4. **\(\sqrt{3153}\)**: Irrational. Since \(3153\) is not a perfect square, its square root is irrational.

5. **\(3\pi\)**: Irrational. Although \(\pi\) is a well-known irrational number, any multiple of it (except zero) remains irrational.

### Summary
- **Rational**: −196, 137299137299
- **Irrational**: \(\sqrt{-196}\), \(\sqrt{3153}\), \(3\pi\)

Would you like further details or explanations on any of these classifications? Here are some follow-up questions you might consider:

1. What defines a rational number?
2. Can you provide examples of both rational and irrational numbers?
3. How do you determine if a square root is rational or irrational?
4. What are some properties of irrational numbers?
5. How is the number \(\pi\) significant in mathematics? 

**Tip**: To determine if a square root is rational, check if the number under the root is a perfect square.

Indicate whether each real number is rational or irrational.

-196

\(\sqrt{-196}\)

137299137299

\(\sqrt{3153}\)

\(3\pi\)

Understand how to classify real numbers as rational or irrational with examples including whole numbers, square roots, and multiples of \(\pi\). This problem covers core concepts in real and imaginary numbers and explains the properties of rational and irrational numbers, suitable for students in Grades 8-10.

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