# Which of the foll

Proof: let us assume that √7 be rational.

then it must in the form of p / q [q ≠ 0] [p and q are co-prime]

√7 = p / q

√7 x q = p

squaring on both sides

7q2= p2 (i)

p2 is divisible by 7

p is divisible by 7

p = 7c [c is a positive integer] [squaring on both sides ]

p2 = 49 c2 (ii)

Substitute p2 in eq (i), we get,

7q2 = 49 c2

q2 = 7c2

q is divisible by 7

Thus q and p have a common factor 7.

As our assumption p & q are co - prime but it has a common factor.

So that √7 is an irrational.

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
RELATED QUESTIONS :

If x is rational RS Aggarwal & V Aggarwal - Mathematics

If <img widRD Sharma - Mathematics

If <img widRD Sharma - Mathematics

The value of <spaRD Sharma - Mathematics

If x =<spaRD Sharma - Mathematics

If <img widRD Sharma - Mathematics

If x = 3+<RD Sharma - Mathematics

The decimal repreRS Aggarwal & V Aggarwal - Mathematics

An irrational numRS Aggarwal & V Aggarwal - Mathematics