If root6 is irrational then prove 5root6 is rational

Dear student,

Let 5root6=be a rational number
therefore ,
5root6=a/b,where b not=0 and a and b are integers

root6=a/5b ...........(1)
​As a,b and 5 are integers ,a/5b is rational ......(2)
so we have,
root6 is rational (from(1)and (2))
But we know root 6 is irrational
therefore our assumption 5root6 is rational is wrong

therefore 5root6 is irrational

Hence proved

Thanks.

Your teacher