Yes, √2 is a real number.
According to the provided reference, real numbers encompass rational numbers, irrational numbers, and integers. The example given explicitly states that √2 is a real number.
To understand this better, let's consider what real numbers are:
- Real numbers include all numbers that can be represented on a number line.
- This includes:
- Rational Numbers: Numbers that can be expressed as a fraction (e.g., 1/2, -3/4, 5).
- Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π). These numbers have infinite, non-repeating decimal representations.
- Integers: Whole numbers and their negatives (e.g., -2, -1, 0, 1, 2).
Since √2 is an irrational number and all irrational numbers are part of the set of real numbers, it is indeed a real number. The approximate value of √2 is 1.41421356..., which is a non-repeating, non-terminating decimal, confirming its irrationality and thus its classification as a real number.
