Question

on a number line√3 was given with the help of √3 write any 4 irrationals that can be constructed​

Answer 1

Answer:

let us assume to the contrary that

$\sqrt{3}$

is a rational

Step-by-step explanation:

that is we can find integers a and b ( not =0 ) such that √3 =a/b squaring both side a^2 =(√3 b^2 )=

√3 divide a

√3 divide a^2

we can write a 3 c for some integer

(3c)^2 =3b^2

9c^2 =3b^2

9/3=b^2

=3/1 = 3c^2 b^2

3 divide b^2

3divide b

there a and b have at lest 3 is common factor but this contracdicts the fact that a and b have no common factor other than. this contracdiction has arisen because of our incorrect assumption that √3 is rational we conclude that √3 is irrational.