What is a Perfect Inquirey Word™?

Question

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.}

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If a word conforms to a special rule, I call it a Perfect Inquirey Word™.
Use the following examples below to find the rule.
Bonus: Which one of the words is a Mega Perfect Inquirey Word™?

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{1.0}} \def\Title{\textbf{ Perfect Inquirey }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ ABDICATED }&\text{ ABDICATE }\\ \hline \text{ BOOGERS}&\text{ BOOGER}\\ \hline \text{ BOSSY}&\text{ SASSY}\\ \hline \text{ DEPLETION }&\text{ REDUCTION}\\ \hline \text{ TRANSLOCATED}&\text{ TELEPORTED}\\ \hline \text{ PERSECUTING}&\text{ OPPRESSING}\\ \hline \text{ CONVULSION}&\text{ CONTRACTION}\\ \hline \text{ COLLEGIATE}&\text{ SCHOLASTIC}\\ \hline \text{ EXCELLENT}&\text{ WONDERFUL}\\ \hline \text{ SIMILAR}&\text{ DIFFERENT}\\ \hline \text{ STATUS}&\text{ STATE}\\ \hline \text{ LACKEY}&\text{ MINION}\\ \hline \text{ TRANSCENDENTALISTS}&\text{ VISIONARIES }\\ \hline \text{ TOWERS}&\text{ TURRETS}\\ \hline \end{array}$$

Hint 1

What is a synonym of "inquire"?

And, if you want to analyze, here is a CSV version:

Perfect Inquirey Words™,Not Perfect Inquirey Words™
ABDICATED,ABDICATE
BOOGERS,BOOGER
BOSSY,SASSY
DEPLETION,REDUCTION
TRANSLOCATED,TELEPORTED
PERSECUTING,OPPRESSING
CONVULSION,CONTRACTION
COLLEGIATE,SCHOLASTIC
EXCELLENT,WONDERFUL
SIMILAR,DIFFERENT
STATUS,STATE
LACKEY,MINION
TRANSCENDENTALISTS,VISIONARIES
TOWERS,TURRETS

Answer 1

I think that a Perfect Inquirey Word is such that

If you convert the word to ASCII and add the numerical values the result is always a perfect square.

Examples

PERSECUTING converted to ASCII is 80 69 82 83 69 67 85 84 73 78 71 80+69+82+83+69+67+85+84+73+78+71 = 841 = 29^2

STATUS converted to ASCII is 83 84 65 84 85 83
83+84+65+84+85+83 = 484 = 22^2

TRANSCENDENTALISTS converted to ASCII is 84 82 65 78 83 67 69 78 68 69 78 84 65 76 73 83 84 83
84+82+65+78+83+67+69+78+68+69+78+84+65+76+73+83+84+83 = 1369 = 37^2

Why are they called Perfect Inquirey

"Perfect" for the perfect square and "Inquirey" could be a synonym for Asky which sounds like ASCII.

Bonus: Which is the Mega Perfect Inquirey Word

I suspect this is STATUS because if we convert it to lower case, then convert to ASCII and add the values, the result is 676 which is also a perfect square.