A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, statistics, and calculus.

Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (π). Other constants are notable more for historical reasons than for their mathematical properties. The more popular constants have been studied throughout the ages and computed to many decimal places.

All named mathematical constants are definable numbers, and usually are also computable numbers (Chaitin's constant being a significant exception).

These are constants which one is likely to encounter during pre-college education in many countries.

The square root of 2, often known as root 2 or Pythagoras' constant, and written as √2, is the unique positive real number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.

Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It is an irrational number, possibly the first number to be known as such, and an algebraic number. Its numerical value truncated to 50 decimal places is:

Alternatively, the quick approximation 99/70 (≈ 1.41429) for the square root of two was frequently used before the common use of electronic calculators and computers. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 7.2 × 10⁻⁵).

Its simple continued fraction is periodic and given by: