Question

Prove that 5/√11 is irrational

Answer 1

Answer:

Assume to reach our contradiction that 5/√11 is rational.

So that 5/√11 can be written as p/q, where p, q are coprime integers and q ≠ 0.

Thus,

p/q=5/√11

Taking the reciprocals...

1/p/q=1/5/√11

=q/p        =√11/5

Here it creates a contradiction that, the LHS p/q is rational while the RHS √11/5 is irrational. Here it seems that √11/5 can be written in fractional form.

Hence our earlier assumption is contradicted and reached the conclusion that 5/√11 is irrational.