It is 5625.
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The perfect square of 75 is 5625. Not sure of the relevance of "greatest", though.
Yes, 5625 is a perfect square. Its square root is 75.
No. The square root of most numbers is irrational - only if the number of which you take the root happen to be perfect squares, do you get a rational root. In this case, to take the square root of 3/4, 3 is not a perfect square, so the root is not rational. Or you can take .75 to be 75/100; once again, 75 is not a perfect square, so the root is irrational.
Not sure what you're asking. Radical means square root, and 75 is not a perfect square. So then we can only right the radical form of 75 as sqrt(75).
Yes, in so far as all numbers are squares (of some number). But it is not a perfect square.