(Q3).Show that 5 - √3 is irrational.

5 - √3

Let us assume 5 - √3 is rational.

That is, we can find co- primes a and b (b ≠ 0) such that 5 - √3 =
a
b
Therefore, 5 -
a
b
 = √3
we get √3 = 5 -
a
b
Since a and b are integers, 5 -
a
b
 is rational, and √3 is also .

But this contradicts that fact that √3 is .

This contradiction has arisen because of our assumption that 5 - √3 is

So 5 - √3 is