Question

prove that root 7 is an irrational

Answer 1

This is the half ans

Answer 2

Think that √7 is a rational number
so √7 = p/q.
(cross multiplication)
√7×q = p

square both sides
(√7×q)² = p²
7 × q² = p²
according to Euclid law (a = p×q+r)
p² is divisible by 7
then p is also divisible by 7
then p is odd number

take that P = 7k
7q² = p²
7q² = (7k)²
7q² = 49k²
q² = 7k²
so q² is divisible by 7
then q is also divisible by 7
then q is odd number

so p and q are odd number because they are divisible by 7
p and q also have the common factor 7

so our think p and q are the prime numbers is wrong
so √7 is is irretional number