Square root of 2

The positive real number whose square is 2. It is irrational and approximately 1.41421356.

Square root: A number that, when multiplied by itself, gives a specified number. Square root of 2 is one specific value produced by this operation.
Unit square: A square whose sides each have length one. Its diagonal has length square root of 2 by the Pythagorean theorem.
Hippasus: A Pythagorean philosopher traditionally associated with the discovery of incommensurable magnitudes. Later accounts connect him to recognizing that a square's diagonal and side are incommensurable.
Diagonal: A line segment joining two nonadjacent vertices of a polygon or polyhedron. The diagonal of a unit square has length square root of 2.
Rational number: A number expressible as the ratio of two integers with a nonzero denominator. No fraction of integers equals square root of 2, although fractions can approximate it.
Irrational number: A real number that cannot be expressed as a ratio of two integers. Its decimal expansion never terminates or repeats, and no such ratio equals it.
Compass-and-straightedge construction: A geometric construction using only an unmarked straightedge and compass. A unit square's diagonal constructs the length square root of 2 exactly.
Pythagoreanism: An ancient Greek philosophical and mathematical tradition associated with Pythagoras and his followers. The discovery of incommensurable lengths challenged its belief that all quantities were rational.
45-45-90 triangle: An isosceles right triangle whose angles measure 45°, 45°, and 90°. With legs of length one, its hypotenuse is square root of 2.
1.414: A terminating decimal approximation to the positive square root of 2. It is a rational approximation, not the exact irrational value.

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