Question

1. Prove that root3 is irrational.

Answer 1

Answer:

let us assume that √3 is rational

i.e.integers a and b is not equal to 0

such that √3=a/b

suppose a and b have common factor 1and we can assume that a and b are coprime

so,b√3=a

squaring both sides

3b^2=a^2

therefore ,a^2is divisible by 3

it is shown that a is also divisible by 3

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

Squaring both sides

a^2=9c^2

substituting value of a,

3b^2=9c^2

i.e. b^2 is divisible by 3 and so b also divisible by 3

therefore a and b have at least 3 common factor

but the fact that a and b are coprime

so, our assuming is wrong i.e. √3 is irrational