Question

prove that$7-\sqrt{15}/4$ is irrational

Answer 1

Let 7-√15/4 be a rational number

Then,

It can be written in the form of p/q as it is rational so,

7-√15/4=p/q

7=p/q+√15/4

As p/q is rational and √15/4 is irrational so teir sum will be irrational.

This means that

7=irrational

But this contadicts the fact that 7 is rational

and this contradiction arise when we assume

7-√15/4 is rational

Hence,7-√15/4 is irrational.