Question

SHOW THAT 2+3 ROOT 5 IS IRRATIONAL

Answer 1

let 3+2 root 5 be rational number
(1)take 3+2 root5 is equal to p upon q
(2) then 2 root 5 is equal to p upon q-3 will come
(3) then 2 root 5 is equal to p-3q upon q will come
(4)then root 5 is equal to p-3q upon 2q will come
Here p-3q is rational but root5 is irrational therefore both can never be equal
Hence 3+2root 5 is irrational