Question

Prove that 3/2root5 is irrational

Answer 1

Hey , here is ur answer

Answer 2

let suppose root5 is rational
therefore. root5=a/b(a and b has only 1 as it common factor)
thus,a=5b
sq.both sides,we get
(a)
$a^{2} = {5b}^{2} \: \: \: \: \: \: (i)$
so a=5c (c is an another integer)
sq.both side,we get

${a}^{2} = 25c$
also a=5b (from i)
thus,5b=25 c
b=5c which is not possible as b has only 1 as its common factor
so our supposition is wrong
therefore,
3/2root5 is irrational