Question

prove that 2-3√5 is an irrational number

Answer 1

Assume 2-3√5 be a rational no
therefore 2-3√5=a/b
hence √5=a-2b/3b
therefore a-2b/3b is a rational no
therefore √5 is a rational no
but we know that √5 is a irrational no
therefore our assumption was wrong that 2-3√5 is a rational no
therefore 2-3√5 is a irrational no

Answer 2

let 2-3√5 be rational number
and 2 is also a rational no.
so,2-3√5-2 is also a rational no.
therefore ,3√5 is a rational
and 3 is also a rational
so, 3√5/3 is also a rational no.
therefore √5 is a
rational
but √5 is an irrational
therefore it is contradiction
so,2-3√5 is an irrational no.proved