Question

prove that root 3 is irrational. plzzzzz ans me gyzzz

Answer 1

hope this helps you ☺☺

Answer 2

Heya here .

_____________________________

If possible , let √3 be rational and let its simplest form be a/b.

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

Now , √3 = a/b
=> 3 = a^2/b^2 [on squaring both side]
=> 3 divides a^2
=> 3 divides a

Let , a = 3c for some integer C.
putting a = 3c in ( i ) , we get

3b^2 = 9c^2
=> b^2 = 3c^2
=> 3 divides b^2
=> 3 divides b

Thus , 3 is a common factor of a and b .
but , this contradict the fact that a and b have no common factor other than 1.

The contradiction arises by assuming that √3 is rational.

Hence , √3 is irrational.
________________________________

$hope \: \: its \: \: helps \: \: you$
✌☺