sqrtkk

sqrtkk is a notation encountered in puzzle literature and informal mathematics discussions to denote the square root of a two-digit repdigit number of the form kk, where k is a decimal digit from 1 to 9. Since kk equals 11k, sqrtkk is often read as sqrt(11k). This is not a standard mathematical operator, but a practical shorthand in certain problem contexts.

Examples and values: for k = 1 to 9, sqrtkk corresponds to sqrt(11), sqrt(22), sqrt(33), sqrt(44), sqrt(55), sqrt(66), sqrt(77), sqrt(88), and sqrt(99). Approximate decimal values are: sqrt(11) ≈ 3.3166; sqrt(22) ≈ 4.6904; sqrt(33) ≈ 5.7446; sqrt(44) ≈ 6.6332; sqrt(55) ≈ 7.4162; sqrt(66) ≈ 8.1240; sqrt(77) ≈ 8.7740; sqrt(88) ≈ 9.3808; sqrt(99) ≈ 9.9499.

Properties: sqrtkk is strictly increasing with k and has no closed form beyond sqrt(11k). It lies between sqrt(11) and sqrt(99). The gaps between successive values decrease as k grows, reflecting the concavity of the square root function.

Usage: In puzzle design and numeric examples, sqrtkk provides simple, non-integer targets for rounding or approximation tasks. It is used to illustrate how a monotone transform of a linear parameter behaves.

Origin and context: sqrtkk is informal; it has no official standardization and is mainly found in problem collections, forums, and educational materials dealing with digits and square roots.

See also: repdigit, square root, numerical approximation.