Enigma 1432: Roman and Arabic
From New Scientist #2593, 3rd March 2007
XVI and LXIV are both Roman numeral perfect squares. If you replace the capital letters consistently with digits, using a different digit for each letter, you can translate XVI and LXIV into Arabic numeral perfect squares, neither of which starts with a zero.
Using the digital values of I, V, X and L that you have discovered;
(1) find another Roman numeral perfect square that uses only these letters (more than one but not necessarily all of them) and translates into an Arabic numeral perfect square;
(2) find a valid Roman numeral that uses only these letters (more than one but not necessarily all of them) and is not itself a perfect square but translates into an Arabic perfect square.
Give the Roman numerals you found in answer to (1) and (2) and the Arabic numerals that each of them translates to.