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.