sqrt1x2

sqrt1x2 is commonly read as the square root of the product 1×2, written as sqrt(1×2) or sqrt(2). In mathematics, the square root function sqrt(x) returns the nonnegative number whose square equals x. For nonnegative x, sqrt(x) is a real number; when x is negative, the square root is defined in the complex numbers.

When the radicand is a product of nonnegative factors, the radical can be separated: sqrt(a×b) = sqrt(a) × sqrt(b). Applying this to 1×2 gives sqrt(1×2) = sqrt(1) × sqrt(2) = 1 × sqrt(2) = sqrt(2). The value sqrt(2) is irrational, meaning it cannot be expressed as a ratio of integers.

Numerically, sqrt(2) ≈ 1.4142135623, with a nonrepeating, nonterminating decimal expansion. The number is famous in geometry as the length of the diagonal of a unit square, by the Pythagorean theorem. It also appears in many areas of science and mathematics as a fundamental constant in problems involving right triangles and Euclidean distance.

Historically, the irrationality of sqrt(2) is a classical result attributed to ancient Greek mathematics, with a standard proof by contradiction often framed around even and odd integers. Related concepts include other square roots, continued fractions, and properties of radicals, as well as alternative interpretations where sqrt(12) would denote a different radical.