By using the method of contradiction verify that P: `sqrt(5)` is irrational.

Explanation

If possbile let `sqrt(5) ` be rational and let its simplest from `a/b`.
Then a and b are intergers having no common factor other than 1 and `b ne 0`
Now `sqrt(5)=a/b rArr 5 =(a^2)/(b^2)` [ on squaring both sider]
`5 b^2 =a^2`
`rArr 5 ` divides `a^2 [ because 5 " divides " 5b^2 ]`
`rArr 5` divides a `[becasue 5` is prime and divides a ]
Let a = 5 c for some integer C.
Putting a= 5 c in (i) we get:
`5b^2=25c^2 rArr b^2=5c^2`
`rArr 5` divides `b^2 [ because 5 " divides " 5c^2]`
`rArr 5 ` divides b [`because` 5 is prime and divides `a^2 rArr 5 ` divides b]
Thus 5 is common factor of a and b.
But this contradicts the fact that a and b have no common factor other than 1.
Hence `sqrt(5)` is irrational .