Question

is the square route of 5/8 rational or irrational?

Answer 1

Square roots are only rational if they are being taken of perfect squares. Do you know how to determine if something is a perfect square?

Answer 2

\[\sqrt{\frac{5}{8}}\]
\[\frac{ \sqrt{5} }{ 2\sqrt{2} }\]
both the square root terms are irrational. so their quotient will also be irrational.