Question

. Prove that there is no rational number whose square is 7.

Answer 1

STEP by STEP explanation:

Let the rational number be a b , whose square is 7 . ... Now , a b 2 = 7 a 2 = 7 b 2 ⇒ a 2 is divisible by 7 ⇒ a is also divisible by 7 Let a = 7 c So , 7 c 2 = 7 b 2 49 c 2 = 7 b 2 7 c 2 = b 2 ⇒ b 2 is divisible by 7 ⇒ b is also divisible by 7 So , a and b have common factor 7 but they were coprime numbers