squarerooted

Squarerooted is an informal term derived from the mathematical square root operation. It can refer to a value that has undergone the square root transformation, or to the act of applying the square root to a number. In strict mathematical writing, one would say “the square root of,” but the term appears in informal or educational contexts to describe results that have been squarerooted.

In mathematical terms, for a real number x ≥ 0, the square root sqrt(x) is the unique nonnegative number y with y^2 = x. When dealing with complex numbers, every nonzero number x has two square roots, ±√x; in this setting the principal square root is typically the nonnegative real root when x is real and nonnegative. The concept of squarerooted therefore depends on the chosen domain and naming conventions.

Key properties include: sqrt(a^2) = |a| for any real a; (sqrt(a))^2 = a for a ≥ 0; sqrt(ab) = sqrt(a) sqrt(b) when a and b are nonnegative, but this multiplicative rule can fail for negative inputs in the real numbers. The square root function is monotone increasing on [0, ∞). In the complex plane, square roots are multi-valued, reflecting the two opposite roots ±z.

Examples: sqrt(16) = 4; sqrt(2) ≈ 1.41421356; sqrt(0) = 0. The value sqrt(n) is rational if and only if n is a perfect square; otherwise it is irrational. Squarerooting appears in geometry, physics, computer science, and statistics, and is subject to numerical considerations such as floating-point precision and rounding in computations.

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