Question

help please..ill give a medal (:
Rationalize the denominator and simplify.

Answer 1

?

Answer 2

\[\sqrt{\frac{ 5m }{ 5n}}\]

Answer 3

To rationalize, we need to multiply by the denominator, to eliminate the radical on the bottom. First, break this up as follows:
\[\frac{ \sqrt{5m} }{ \sqrt{5n} }\] Now multiply top and bottom by rad 5n. This rationalizes it.
\[\frac{ \sqrt{5m} }{ \sqrt{5n} }\ \times \frac{ \sqrt{5n} }{ \sqrt{5n} } = \frac{ \sqrt{25mn} }{ 5n } = \frac{ 5\sqrt{nm} }{ 5n } = \frac{ \sqrt{nm} }{ n }\]