Question

prove that 2√3 is irrational number

Answer 1

irrational number multiplied by rational number gives the product as irrational. 2 is rational multipled by
$\sqrt{ 3 }$

Answer 2

let us assume that 2√3 is a rational no.
2√3=a/b(where a Nd b are co prime no.)
squaring both side
12=a^2/b^2
12b^2=a^2............k
12 is a factor of a^2
12 will be factor of a.....................1
let a=12c
squaring both side
a^2=144c^2...................ll
putting ll in k
12b^2=144c^2
b^2=12c^2
12 is a factor of b^2
12 will be factor of b..............lll
from 1&lll
12 is the factor of both a&b
so, they are not co prime no.
hence our assumption is wrong
2√3 is an irrational no.