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# State whether the following statement is true or false.All real numbers are irrational.A. TRUEB. FALSE

Last updated date: 20th Jun 2024
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Hint: Using the definitions of real numbers and irrational numbers we check if all real numbers are irrational or not.

Rational numbers are the numbers that can be written in the form $\dfrac{p}{q}$ where $q$ is non-zero and both the numerator and denominator are integers, i.e. the decimal representation of a rational number is either terminating or recurring. Examples: $\dfrac{1}{2},\dfrac{0}{5},\sqrt 4 = \pm 2,7$etc.
An irrational number is a number that cannot be represented in the form $\dfrac{p}{q}$, and the value of an irrational number has the decimal representation as non-recurring, non-repeating and non-terminating. Also, any number that is not a rational number is called an irrational number. Examples: $\sqrt 2 ,\sqrt 3 ,\pi$etc.