What is the square root of 2?

The square root of 2, often written as √2, is a positive real number that, when multiplied by itself, equals 2.

  • Value: Its numerical value, truncated to 6 decimal places, is approximately 1.414214. The decimal%20representation of √2 is infinite and non-repeating, making it an irrational number.

  • Irrationality: √2 is a classic example of an irrational%20number. Its irrationality was supposedly discovered by Hippasus of Metapontum, a Pythagorean. The proof of its irrationality often involves proof by contradiction.

  • Algebraic Number: √2 is an algebraic%20number, specifically a root of the polynomial equation x² - 2 = 0.

  • Geometric Significance: Geometrically, √2 is the length of the diagonal of a square with sides of length 1. This relationship is a direct consequence of the Pythagorean%20theorem. It also represents the ratio between the diagonal and a side of a square.

  • Trigonometry: In trigonometry, √2 appears in the values of certain trigonometric functions for angles of 45 degrees (π/4 radians). For instance, sin(45°) = cos(45°) = 1/√2 = √2/2.