A unary function from quantities to quantities that is the arithmetical operation that takes a (non-negative) number to its non-negative square root, extended to measurable ScalarIntervals generally. (Square Root Fn SCALAR) is by definition equal to ROOT: the non-negative quantity or number such that (Times Fn ROOT ROOT) is equal to SCALAR.

For example, (Square Root Fn 81) is equal to 9 and (Square Root Fn (square mile 9)) is equal to (mile 3).

Note that while this holds:

  (Inverse Quant Functions Nonsymmetric Squared Fn Square Root Fn) ,

this does not:

  (Inverse Quant Functions Nonsymmetric Square Root Fn Squared Fn) .

For the square of the non-negative square root of X is always X, but the non-negative square root of the square of X is not always X (e.g. where X is -2). Thus, Square Root Fn and Squared Fn might be considered quasi-inverses .