Q. 19 B5.0( 1 Vote )

Prove that the fo

Answer :

Let us consider that 2/√7 is a rational number.

Let 2/√7 = a/b for b ≠ 0 ……………… (i)


Where a and b are co-prime integer numbers.


From (i) we can write as follows:


2b/a = √7


Now from the LHS we know that a and b are integral numbers and therefore the fraction will also be rational number which implies that √7 has to be a rational number. But we know that √7 is an irrational number.


So our assumption at the beginning of the problem is proved false.


So 2/√7 is an irrational number.


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 :

Prove that the foRajasthan Board Mathematics

What can you say Rajasthan Board Mathematics

Prove that the foRajasthan Board Mathematics

Prove that the foRajasthan Board Mathematics

If p and q are coRajasthan Board Mathematics

Prove that the foRajasthan Board Mathematics

Prove that the foRajasthan Board Mathematics

Prove that the foRajasthan Board Mathematics

The decimal expanRajasthan Board Mathematics

For the decimal eRajasthan Board Mathematics