A. is the answer it can't be rational
Explanation:
√21 is irrational.
Let's assume that √21 is rational. So √21 can be expressed in the form p/q form.
p/q is the reduced form of rational number so p and q have no common factors other than 1, i.e. they are co-prime numbers.
√21 = p/q
21 = p^2/q^2... (squaring both the sides)
21q^2 = p^2
p^2 is even. p^2 is a factor of 2...(1)
p=2t p^2=4t^2 t belongs to I
2q^2 = 4t^2 (2q^2=p^2)
q^2 = 2t^2
q^2 is even
q is even
2 is a factor of q.
From the statements (1) and (2), 2 is a common factor of p and q both.
This is contradictory because in p/q, we have assumed that p and q have no common factors other than 1.
That is, our assumption that √21 is rational is wrong.
Therefore, √21 is irrational.