Let's classify each number as either rational or irrational, and explain why:

1. $\frac{2}{3}$:

   • Rational. A rational number is any number that can be expressed as a fraction of two integers. Since $\frac{2}{3}$ is a fraction, it is a rational number.

2. $\sqrt{25}$:

   • Rational. The square root of 25 is 5, which is a whole number (integer). All integers are rational numbers because they can be written as fractions (e.g., $5 = \frac{5}{1}$).

3. $-0.75$:

   • Rational. $-0.75$ is a terminating decimal, and all terminating decimals are rational numbers because they can be written as fractions (in this case, $-0.75 = \frac{-3}{4}$).

4. $\sqrt{2}$:

   • Irrational. The square root of 2 cannot be expressed as a fraction of two integers, and its decimal expansion is non-terminating and non-repeating. Therefore, $\sqrt{2}$ is an irrational number.

5. 7,548,123:

   • Rational. This is a whole number (integer), and all integers are rational numbers because they can be expressed as fractions (e.g., $7,548,123 = \frac{7,548,123}{1}$).

Summary:

• $\frac{2}{3}$ → Rational
• $\sqrt{25}$ → Rational
• $-0.75$ → Rational
• $\sqrt{2}$ → Irrational
• 7,548,123 → Rational

Would you like any further details or explanations? Here are five related questions to explore further:

1. What is the difference between rational and irrational numbers?
2. How can you prove that $\sqrt{2}$ is irrational?
3. Can repeating decimals be classified as rational?
4. How do you classify the sum or product of rational and irrational numbers?
5. Are all square roots of perfect squares rational?

Tip: Any decimal that either terminates or repeats is always a rational number.