Q. 54.2( 53 Votes )

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Answer :

To prove :  is an irrational number.
Solution:
Let assume that is rational.


Therefore it can be expressed in the form of , where p and q are integers and q≠0


Therefore we can write =


2√3= 5 -
⇒ √3 = 


is a rational number as p and q are integers. This contradicts the fact that √3 is irrational,
so our assumption is incorrect. Therefore is irrational.
Note: Sometimes when something needs to be proved, prove it by contradiction.
Where you are asked to prove that a number is irrational prove it by assuming that it is rational number
and then contradict it.

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