Question

To prove root3 is an irrational number​

Answer 1

• theorem 1.3 is if a prime number divides a square ,then it divides a.

hope it helps.

Answer 2

let us suppose that √3 is rational and =a/b where a and b are coprime

√3=a/b

b√3=a

squaring both sides

3b²=a²

therefore a² is divisible by 3 so a is also divisible by 3

let us take a=3c

3b²=9c²

b²=3c

therefore b² is divisible by 3  so b is also divisible by three

now we got to know that a and b must be having atleast three as their common factor but a and b are coprime

this contradiction is arised from our incorrect assumption that √3 is rational

so we conclude that √3 is irrational