Question

Prove that 4+√5 is irrational

Answer 1

Hey friend here is your answer,

Let 4+root 5 be an rational number.
So 4+root 5 = p/q

So root5 = p/q-4

= root5 = (p-4q)/q

Now as we have taken p and q are rational numbers and 4 is also a rational number.

We know substraction and division between any 2 rational no. is rational number so,

RHS is rational but LHS is root 5 which is irrational.

Hence, it is a contradiction so p and q are irrational so, 4+ root 5 is also irrational.

Hope it helps you a lot