Question

Prove that √8 is irrational

Answer 1

Answer:

Step-by-step explanation:

The factor of underrot 8 is

2underrot3

So

We can say that it's a irrational no

Answer 2

Step-by-step:

If possible let √8 be rational and its simplest form be a/b.

Then, a and b are integers having no common factor other than 1 and b≠0.

Now, √8=a/b=>8=a²/b²(on squaring both sides)

=>8b²=a²

=>8 divides a²(since, 8 divides 8b²)

=>8 divides a

Thus , 8 is a common factor of a and b.

But, this contradicts the fact that a and b have no common factor other than 1.

This contradiction arises by assuming that √8 is rational.

Hence, √8 is irrational.

:-):-)

HOPITHLPS!!!!