Question

prove that 3-2root5 is an irrational number

Answer 1

let 3 - 2 root 5 is rational therefore 3 + 2 root 5=a/b root 5=a-3/2b because  a-3/2b is rational therefore root 5 will also be rational but we know that, root 5 is irrational that is our supposition is wrong that is 3-2 root 5 is irrational.........
hope its help u.......

Answer 2

let 3-2root5=rational
3-2root5 =p/q
3=p/q+2root5
q transfer to that side and get multiply with 3 and p comes in denominator.
3q/p=2root5
3q/2p=rooot5
since root 5 is irrartional then 3q/2p is also irrational
therefore if whole quantity is irrational then 3-2root5 is also irrational.