no 5 one pls I need this urgently

Answers
Let us consider 2 be a rational number, then
2=p/q, where ‘p’ and ‘q’ are integers, q=0 and p, q have no common factors (except 1).
So,
2=p2/q2
p2=2q2 …. (1)
As we know, ‘2’ divides 2q2, so ‘2’ divides p2 as well. Hence, ‘2’ is prime.
So 2 divides p
Now, let p=2k, where ‘k’ is an integer
Square on both sides, we get
p2=4k2
2q2=4k2 [Since, p2=2q2, from equation (1)]
q2=2k2
As we know, ‘2’ divides 2k2, so ‘2’ divides q2 as well. But ‘2’ is prime.
So 2 divides q
Thus, p and q have a common factor of 2. This statement contradicts that ‘p’ and ‘q’ has no common factors (except 1).
We can say that 2 is not a rational number.
2 is an irrational number.
Now, let us assume 3−2 be a rational number, ‘r’
So, 3−2=r
3–r=2
We know that, ‘r’ is rational, ‘3−r’ is rational, so ‘2’ is also rational.
This contradicts the statement that 2 is irrational.
So, 3−2 is an irrational number.
Hence proved