Question

which of the following is true about irrational numbers? a. some irrational numbers are natural numbers. b. irrational numbers include decimals with a repeating pattern. c. the square root of every non - perfect square will be an irrational number. d. irrational numbers will never be real numbers.

Explanation:

1. Natural numbers are positive integers (1, 2, 3...), and irrational numbers cannot be expressed as a fraction of two integers. So, irrational numbers are not natural numbers.
2. Decimals with a repeating pattern are rational numbers, not irrational numbers. Rational numbers can be written as fractions, and repeating - decimals can be converted to fractions.
3. The square root of a non - perfect square (a number that is not the square of an integer) cannot be written as a fraction of two integers, so it is an irrational number. For example, $\sqrt{2}$, $\sqrt{3}$, etc.
4. Irrational numbers are a subset of real numbers. Real numbers include both rational and irrational numbers.

Answer:

C. The square root of every non - perfect square will be an irrational number.