Question

Prove that r5 is irrational​

Answer 1

Let 5 be a rational number.

then it must be in form of qp where, q=0 ( p and q are co-prime)

p2 is divisible by 5.

So, p is divisible by 5.

So, q is divisible by 5.

Thus p and q have a common factor of 5.

We have assumed p and q are co-prime but here they a common factor of 5.

Answer 2

Answer:

√5 decimal expansion is non terminating non repeating. So it is an irrational number.