Rationalize and simplify square root of 5m over square root of 5n

√5m/√5n

so here you have to rationalize it by making the denominator not a root. and to do that the easiest way is to multiply it by itself.

*but when you multiply you multiply it to both numerator and denominator

√5m*√5n:√5n*√5n

then multiply

√25mn:√25n^2

√5·5·m·n/√5·5·n·n

then simplify

5√mn/5n

√mn/n

You have to multiply the numerator and denominator by the conjugate (square root of 5n) and reduce to get: (square root of mn) over n.