Find the 453root

Let we asume that √3 is rational i.e it can be qritten as a/b. √3=a/b(where a and b are co prime ). squaring on both sides. (√3)square=(a/b) square. 3= a square/b square. 3b square=a square______(1). 3 divides a square so 3 divides a also. a=3c_____________(2). from 1 and 2 equation. 3c square=3b square 3c square=b square. __________(3) 3divides b square so 3 divides b also. from 2 and 3 wquation it is proved that 3 is a common factor of a and b,which is a contradiction of our assumption this is due ti our wrong assumption .Si √3 is irrational number

Prove that √3 is irrational