Question

Prove that √3 is irrational.​

Answer 1

Step-by-step explanation:

let us assume root 3 is rational then it can be witten in the form a/b,where a and a are integers and co primes. then

√3=a/b

√3b=a

square

(√3b) ^2=a^2

3 divides a^2(since a^is a multiple of 3)

3 divides a (theorem 1.3)

here a can be also be written as

a=3c

therefore

(3c) ^2=3b^2

9c^2=3b^2

divide by 3

3c^2=b^2

therefore 3 divides b^2( b^2 is a multiple of 3

3 divides b (theorem 1.3)

from this we can say √3 is rational but ot is a contradiction due to our wrong assumption