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For a chi-square test there is a null hypothesis which describes some distribution for the variable that is being tested. The expected frequency for a particular cell is the number of observations that would be expected in that cell if the null hypothesis were true.
The F-test (when used in an Analysis of Variance Problem): F = Mean square between / Mean square within If F=1, Mean square within and Mean square between are almost equal.
Not sure what you mean by "perfect square root".A "perfect square" is the square of a whole number; if that's what you mean, yes, it's the square of the number 1.
No!
When you multiply a number by itself, you square the number. The square of 3 is 9.