Programming puzzle: Symplifying (simple) fractions containing square roots

[Han]

Are you aware that the HP50G can handle "exact" integers of "infinite" size (up to the limit of RAM)? The problem can be solved with just a few lines of code since the HP50G handles integers natively.

\[ \frac{a\sqrt{b}}{c\sqrt{d}} = \sqrt{\frac{a^2\cdot b}{c^2\cdot d}} \]

So compute \(\frac{a^2\cdot b }{c^2\cdot d} \) and take the square root. Just make sure you use exact integers as inputs.

EDIT: a b c d SWAP SQ * ROT SQ ROT * SWAP / \( \sqrt{\quad} \)

Extracting the integers is left as an exercise for the reader (but it too is a fairly short snippet of code)