Question

2/under root 7 is a irrational

Answer 1

Let 2/√7 be a rational number.

A rational number can be written in the form of p/q.

2/√7 = p/q

√7/2 = q/p

√7 = 2q/p

p,q are integers then 2q/p is a rational number.

Then √7 is also a rational number.

But this contradicts the fact that √7 is an irrational number.

So,our supposition is false.

Therefore,2/√7 is an irrational number.

Hence proved.

Hope it helps....

Answer 2

Hi there !!

To prove :-
2/√7 is irrational

Lets assume that 2/√7 is rational

Let , 
2/√7 = r , where r is rational

√7/2 = 1/r 

√7 = 2/r

Here , 
RHS  is purely rational .
Whereas on the other hand , LHS is irrational
This is a contradiction
Hence , our assumption was wrong

∴2/√7 is irrational