Question

prove √3 is an irrational number​

Answer 1

Hope it's helpful to you.

Please mark as Brainlist answer.

Answer 2

Answer:

Plz mark as brainalist if it is helpfull to you.

Assume that root 3 is rational

So, root 3 =a/b ( where a and b are

co- prime)

(root 3b)^2 = a

3b^2 = a .........(eqn 1)

Now, 3 divides a^2 therefoe by theorum 1.3 3divides a.

Let, a/3 = c (where c is some

integer)

a = 3c

by putting a= 3c in (eqn 1)

3b^2 = (3c)^2

3b^2 = 9 c^2

b^2 = 3c ^2

Now,3 divides b^2. Therefore, by theorum 1.3 3 divides b

This contradicts that our assumption is wrong ant root 3 is irrational.

HOPE IT HELPS YOU

Plz mark as brainalist.