Question 1074443
So we're looking for perfect squares between 500 and 1000, divisible by 2 as well as by 3 (—> which means divisible by 6).  Let's scan the "square roots" {{{ sqrt(n) }}} that correspond to  {{{ 500<=n<=1000 }}}.  Note that for n to be divisible by 6, {{{ sqrt(n) }}} must also be divisible by 6, because we are considering squares whose roots are whole numbers (no irrationals):
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22^2 = 484  <<< Too small, outside of range
23^2 = 529  <<<  529 is the first candidate, but it is not divisible by 2 or 3
24^2 = 576   (576 is one number)
(skip ahead to 30, because its the next number divisible by 6)
30^2 = 900  (900 is another number)
(skip ahead to 36)
36^2 = 1296 > 1000,  too big, outside of range  (we're done)

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Ans:  Two numbers between 500 and 1000 are divisible by 2 and 3 and have whole number square roots.  Those two numbers are 576 and 900.
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