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Question

State whether the following statement are true or false. Justify your answer. Every real number is an irrational number.


A
True
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B
False
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Solution

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 pq. Example : 25,10,13,12,...
  • A number s is called irrational, if it cannot be written in the form pq. Example : 3,5,π,1.3333...,
    where p and q are integers and q0.

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.


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