Final answer:
The numbers given are evaluated to determine if they are integers, rational numbers, or irrational numbers. The numbers 5, -√4, and 15 are integers, 2√3 is an irrational number, and 0.81 is a rational number that is not an integer.
Step-by-step explanation:
To determine whether each number is an integer, a rational number that is not an integer, or an irrational number, we'll evaluate each given number.
- Integers are whole numbers that can be positive, negative or zero, but without any fractional or decimal part.
- Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers (the denominator cannot be zero). They may be integers, fractions, or decimal numbers with a finite number of digits or a repeating pattern.
- Irrational numbers cannot be expressed as simple fractions and have decimal expansions that do not terminate and do not repeat.
- Evaluation of Each Number:
- 5 - This is an integer.
- -√4 - Since √4 equals 2 and the negative of a whole number is still an integer, -2 is an integer.
- 2√3 - Because the square root of 3 is an irrational number, multiplying it by 2 still results in an irrational number.
- 15 - This is clearly an integer.
- 0.81 - This is a rational number because it is a decimal that has a finite number of digits and can be expressed as a fraction 81/100.