Here are five questions based on real numbers:

1. Classification: Identify whether the following numbers are rational or irrational:

   • $\sqrt{16}$, $\frac{22}{7}$, $\pi$, $-3.75$, $0.1010010001...$

2. Operations: If $a = 3.5$ and $b = -2.1$, compute $a + b$, $a - b$, $ab$, and $\frac{a}{b}$.

3. Properties: Prove that the sum of two rational numbers is always rational. Does the same rule apply to irrational numbers? Why or why not?

4. Intervals: Express the following sets using interval notation:

   • All real numbers greater than 2 and less than or equal to 10.
   • All real numbers less than -5 or greater than 3.
   • All real numbers except 0.

5. Square Roots and Approximations: Without using a calculator, estimate $\sqrt{50}$ to two decimal places and explain your method.

Tip:

Every rational number can be written as a fraction of two integers, while irrational numbers cannot be expressed this way (e.g., $\pi$, $\sqrt{2}$).

Would you like detailed solutions for any of these? 😊