Question

Prove that root 3 - root 2 is irrational.​

Answer 1

Step-by-step explanation:

let us assume, to the contrary that root3 is rational

√3=a/b

so b√3=a

squaring on both the sides therefor, a square is divisible by 3 and theorem 1.3 ,it follows that a is also divisible by 3

so we can write a=3c for some integer c

sabstituing for a

we get 3b square = 9c square that is b square =3c square

this means that b square is divisible by 3 ,and so b is also divisible by 3

therefore, a and b have least 3 as a common factor

but this show that a and b are coprime

this contradicts that our assumption is wrong that √3 ur rational

so we concluded that √3 Is irrational

same for √2 also