4. Which statement is true? (1 point)
Every rational number is a perfect square.
Every rational number is a real number.
Every integer is an irrational number.
Every real number is an integer.
To determine which statement is true, we need to understand the definitions of rational numbers, perfect squares, real numbers, integers, and irrational numbers.
1. A rational number is any number that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. For example, 1/2, -3/4, and 5/1 are rational numbers.
2. A perfect square is an integer that can be obtained by squaring another integer. For example, 4 is a perfect square because it can be obtained by squaring 2: 2^2 = 4.
3. A real number is any number that can be represented on the number line, including rational and irrational numbers. Examples of real numbers are 3.14, -2, and √2.
4. An integer is a whole number that can be positive, negative, or zero. Examples of integers are -5, 0, and 7.
5. An irrational number is any number that cannot be expressed as a fraction of two integers. Examples of irrational numbers are π (pi) and √2.
Now, let's evaluate each statement:
Statement 1: Every rational number is a perfect square.
This statement is not true. Rational numbers include fractions, which are typically not perfect squares. For example, 1/2 is a rational number but not a perfect square.
Statement 2: Every rational number is a real number.
This statement is true. The set of rational numbers is a subset of the set of real numbers, meaning that every rational number is indeed a real number.
Statement 3: Every integer is an irrational number.
This statement is not true. Integers are a different type of number, representing whole numbers. While some integers (like √2) can be irrational, not all integers are irrational.
Statement 4: Every real number is an integer.
This statement is not true. Real numbers include both integers (whole numbers) and non-integers (fractions and irrational numbers). So, while every integer is a real number, not every real number is an integer.
Therefore, the correct answer is:
Statement 2: Every rational number is a real number.