Yes.
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118 is a rational number
As much as, in these days of uncertainty, anything can be anything. As long as the constraints of a rational number are kept to, a rational number will always remain a rational number.
The square root of 118 is not a whole number - the closest square number to 118 is 121 - which is 11 squared.
Yes.
Yes, but only if the rational number is 0.