Square root of 6

Square root of 6
Rationality	Irrational
Representations
Decimal	2.449489742783178098...
Algebraic form
Continued fraction

Distances between vertices of a double unit cube are square roots of the first six natural numbers. ( $\sqrt7$ is not possible due to Legendre's three-square theorem.)

The square root of 6 is the positive real number that, when multiplied by itself, gives the natural number 6. It is more precisely called the principal square root of 6, to distinguish it from the negative number with the same property. This number appears in numerous geometric and number-theoretic contexts.

It is an irrational algebraic number. The first thirty significant digits of its decimal expansion are:

2.44948974278317809819728407471....

which can be rounded up to 2.45 to within about 99.98% accuracy (about 1 part in 4800).

Since 6 is the product of 2 and 3, the square root of 6 is the geometric mean of 2 and 3, and is the product of the square root of 2 and the square root of 3, both of which are irrational algebraic numbers.

NASA has published more than a million decimal digits of the square root of six.

A Logarex system Darmstadt slide rule with 7 and 6 on A and B scales, and square roots of 6 and of 7 on C and D scales, which can be read as slightly less than 2.45 and somewhat more than 2.64, respectively