Q. 54.2( 53 Votes )

Show that <img st

Answer :

To prove :  is an irrational number.
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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

<span lang="EN-USRS Aggarwal - Mathematics