Question

prove that 3 + 2 root 5 is an irrational number

Answer 1

Let's assume that 3+2root 5 is rational
3+2root 5=a/b(a and b are coprime)
2root 5=a-3b /b
Now
Root 5 =a-3b/2b
But we know that root 5 is irrational
Therefore our assumption is wrong
Hence 3+2root 5 is irrational


Hence proved

Answer 2

let 3 + 2 root 5 is rational 
therefore 3 + 2 root 5=a/b(where a and b are co prime integer ) 
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 assumption is wrong 
that is 3+2 root 5 is irrational