Answer :

Let us assume that is a rational number.


For a number to be rational, it must be able to express it in the form where p and q do not have any common factor, i.e. they are co-prime in nature.


Since is rational, we can write it as




[ squaring both sides ]



Thus, p2 must be divisible by 3. Hence p will also be divisible by 3.


We can write p = 3c ( c is a constant ), p2 = 9c2


Putting this back in the equation,





Thus, q2 must also be divisible by 3, which implies that q will also be divisible by 3.


This means that both p and q are divisible by 3 which proves that they are not co-prime and hence the condition for rationality has not been met. Thus, is not rational.


is irrational.


Hence, the statement p: is irrational , is true.


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
caricature
view all courses
RELATED QUESTIONS :

Use contradictionRS Aggarwal - Mathematics

By giving a countRS Aggarwal - Mathematics

Consider the statRS Aggarwal - Mathematics

Let p : If x is aRS Aggarwal - Mathematics

Check the validitMathematics - Exemplar

Check the validitMathematics - Exemplar

Prove the followiMathematics - Exemplar