a rational number can be written in the form a/b where a and b are integers and b≠0
so
remember that √(a/b)=(√a)/(√b)
so[tex]\sqrt{\frac{82}{20}}=\sqrt{\frac{41}{10}}=\frac{\sqrt{41}}{\sqrt{10}}\frac{\sqrt{410}}{10}[/tex]
we can't make it into a/b so it's irrational
