Prove that `sqrt(n)` is not a rational number. if `n` is not a perfect square.

Explanation

Let , us assume that `sqrtn` is rational
so, `sqrtn = a/b` where a and b are integers and b is not equation to zero .
Let, a/b are co- prime taking square both side ,we get
`n = a^2/b^2`
`nb^2 = a^2 ......(1)`
so, n divide `a^2`
it means n also divide `a`
for some integer` c`
`a = nc`
now squaring both side
`a^2 = n^2c^2`
`nb^2 = n^2c^2` [ from (1) ]
`b^2 = nc^2`
so , `n` divide `b^2`
it means b also divide b
so, a and b have n as a prime factor
but this contradict the fact that a and b are co- prime .
therefore , our assumption is wrong
hence,` sqrtn` is irrational