1. **Stating the problem:** We need to classify each number in the table according to the categories: Real, Non-real, Rational, Irrational, Prime, Integer, and Number. 2. **Important definitions and rules:** - Real numbers include all rational and irrational numbers. - Non-real numbers are numbers that are not real (e.g., involving imaginary units). - Rational numbers can be expressed as a fraction $\frac{a}{b}$ where $a,b$ are integers and $b \neq 0$. - Irrational numbers cannot be expressed as such fractions. - Prime numbers are natural numbers greater than 1 with only two divisors: 1 and itself. - Integers are whole numbers including negatives, zero, and positives. - All these are subsets of numbers. 3. **Classifying each number:** | Number | Real | Non-real | Rational | Irrational | Prime | Integer | Number | |--------|-------|----------|---------|------------|-------|---------|--------| | 0.5 | $\checkmark$ | | $\checkmark$ | | | | $\checkmark$ | | $\pi$ | $\checkmark$ | | | $\checkmark$ | | | $\checkmark$ | | $\sqrt{8}$ | $\checkmark$ | | | $\checkmark$ | | | $\checkmark$ | | 1.25 | $\checkmark$ | | $\checkmark$ | | | | $\checkmark$ | | $\sqrt{-16}$ | | $\checkmark$ | | | | | | | -12 | $\checkmark$ | | $\checkmark$ | | | $\checkmark$ | $\checkmark$ | | $\frac{1}{4}$ | $\checkmark$ | | $\checkmark$ | | | | $\checkmark$ | | $\sqrt[3]{8}$ | $\checkmark$ | | $\checkmark$ | | | | $\checkmark$ | | 7 | $\checkmark$ | | $\checkmark$ | | $\checkmark$ | $\checkmark$ | $\checkmark$ | 4. **Explanation:** - 0.5 is a rational real number. - $\pi$ is a real irrational number. - $\sqrt{8} = 2\sqrt{2}$ is irrational and real. - 1.25 is rational and real. - $\sqrt{-16}$ is non-real (imaginary). - -12 is an integer, rational, and real. - $\frac{1}{4}$ is rational and real. - $\sqrt[3]{8} = 2$ is rational, integer, and real. - 7 is prime, integer, rational, and real. All except $\sqrt{-16}$ are real numbers.