sqrt502

sqrt502 denotes the positive square root of the integer 502. It is the real number r such that r squared equals 502. Since 502 factors as 2 × 251 and is not a perfect square, sqrt(502) is irrational and cannot be expressed as a fraction of integers.

In exact form, sqrt(502) is already in its simplest radical expression and does not simplify to a smaller surd. The number lies between 22 and 23, since 22^2 = 484 and 23^2 = 529.

A numerical approximation is commonly used in practical calculations. sqrt(502) ≈ 22.40536 (to five decimal places). More digits can be obtained with a calculator, but the value remains irrational and non-repeating.

Context and uses: sqrt(502) can appear in problems involving geometric lengths, such as the side length of a square with area 502, or in algebraic contexts where expressions involve square roots of integers. It serves as an example of a non-square radical that cannot be simplified further.

Related concepts include the general notion of square roots, irrational numbers, and the properties of radicals. While sqrt(502) has no special constants or closed-form simplifications, it is part of the broader set of square roots of non-square integers.