Question

show that√7 is rational​

Answer 1

let √7 be a rational number such that

√7 = a/b ... where a & b are co primes

√7 = a/b

=>7 = a²/b²

=> a²= 7b² ...(1)

=> 7 is a factor of a² as well as of b

=> a = 7K ...(2)

From (1) and (2)

49k²= 7b²

=> b²= 7k²

=> 7 is is a factor of a as well as of b

but a & b were co primes

This contradicts our assumption that √7 is rational .

Hence, √7 is irrational