Question

Show that 5-2√3 is irrational

Answer 1

5-2√3 is irrational because the difference or sum of a rational or irrational or two irrationals is always an irrational.

Answer 2

Answer:

assume that 5-2√3 is a rational number

So it can be written in the form of p/q i.e.

5-2√3=p/q

=> -2√3=p/q-5

=> -2√3=p-5q/q

=> √3=-(p-5q)/2q

Here p and q are integers,hence -(p-5q)/2q must be a rational number. But it is equal to √3 which is an irrational no.

Hence this contradicts

This contradiction has arisen because of our wrong assumption i.e. 5-2√3 is rational

Hence 5-2√3 is a irrational no.