Question

prove that (2-7√3) is an irrational number, where √3 is irrational​

Answer 1

Answer:

let's consider 2-7√3 is rational,

then,

2-7√3 = p/q(where p and q are integers and q is not zero)

=> -7√3=p-2q/q

=> √3=-(p-2q)/7q

Thus it proves that √3 is rational as -(p-2q)/7q is rational but it is given that √3 is irrational .

As this contradicts our consideration, it is proved that 2-7√3 is irrational