Question

State whether the following statement is true or false: All real numbers are irrational.

• A. True
• B. False

Answer 1

The correct option is B False

Define Real numbers, rational and irrational number.

• The collection of both rational and irrational numbers is called real numbers.
• A number $‘s’$ is called rational, if it can be written in the form $\frac{p}{q}$. Example : $25,10,13,\frac{1}{2},...$
• A number $‘s’$ is called irrational, if it cannot be written in the form $\frac{p}{q}$. Example : $\sqrt{3},\sqrt{5},\sqrt{\pi },1.3333...,$
  where $p$ and $q$ are integers and $q\ne 0.$

Therefore every irrational number is a real number whereas every real number is not an irrational number.

Hence the statement “ Every real number is an irrational number.” is false.