Question

prove that √5 is irrational​

Answer 1

Answer:

Let √5 Bea rational number.

Then it must be in form of p/q where q not equal 0 (p and q are co-prime )

√5=p/q

√5×q=p

suaring on both side.

5q^2=p^2---------------(1)

put p^2 i. eq.(1)

So, q is divisible by 5.

.

Thus p and q have a common factor of 5.

So, there is a contradiction as per our assumption.

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

The above statement contradicts our assumption.

Therefore, √5 is an irrational number.