Question

prove root 7 is irrational no

Answer 1

we can prove this by proving that the if go for long division method of 7 so it is non terminating or non repeating and can't be described in the form of p/q

Answer 2

Let √7 be rational Then, √7 = a/b (a, b are co-primes) Squaring both sides  7 = a^2/b^2 7b^2 = a^2....(1) •7 divides a^2 •7 divides a Putting a=7c in (1) 7b^2 = 49c^2 {a^2 = (7c)^2} b^2 = 7c^2....(2) •7 divides b^2 •7 divides b But (1) and (2) contradicts the fact that a and b are co-primes. Therefore √7 is irrational.