"Square number" is the term we use for a number which is the square of a whole number. Examples include $4,$ $65536,$ $1,$ and $0.$

Squares in many different contexts - I look forward to people listing some examples.

Related:
FermatNumber
PythagorasTheorem
RationalisingTheDenominator
(none) AGentleIntroductionToNPC
ContinuumHypothesis
GeorgCantor
RationalNumber
TimeComplexity
TransfiniteNumbers
UncountableSet
DifferenceOfTwoSquares
TypesOfNumber
AGentleIntroductionToTimeComplexity
CountableSet

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SquareNumber
WholeNumber
AlgebraicNumber
CategoryMetaTopic
Commutative
ComplexNumber
ImaginaryNumber
IrrationalNumber
Matrices
PerfectNumber