Question

prove that 3+2root5 are irrational

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=a/b
2root5=a/b-3
rearranging the equation  2root5=a-3b/b
root5=a-3b/2b
from the above we observe that a-3b/2b is rational number.so that root5is also rational.but root5 is not rational number.by this we can say 3+2root5 is irrational number