Question

Prove that 8 is an irrational number ​

Answer 1

I think it is irrational number
Mark me as a brainlist

Answer 2

Answer:

Hey mate your question is wrong, as 8 is a rational no. If it was supposed to be √8 and has a typing mistake, then I am providing its solution below.

Explanation:

The proof has been given by the method of contradiction.

suppose √8 = a/b with integers a, b  (b ≠ 0)

and GCD (a,b) = 1 (meaning the ratio is simplified)

then 8 = a²/b²

and 8b² = a²

⇒ 8 divides a²

⇒ 8 divides a

So, there exists a 'p' within the integers such that:

a = 8p

and thus,

⇒ √8 = 8p/b

⇒ 8 = 64p²/b²

⇒ 1/8 = p²/b²

⇒ b²/p² = 8

⇒ b² = 8p²

⇒ 8 divides b² which means 8 divides b.

⇒ 8 divides a, and 8 divides b, which is a contradiction because

GCD(a, b) = 1

Therefore, √8 is irrational.

Hope this helps.....