Square Root of 3

The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property. It is denoted by

The first sixty significant digits of its decimal expansion are:

1.73205 08075 68877 29352 74463 41505 87236 69428 05253 81038 06280 5580... (sequence A002194 in OEIS)

The rounded value of 1.732 is correct to within 0.01% of the actual value. A close fraction is (1.732142857...).

Archimedes reported (1351/780)2 > 3 > (265/153)2, accurate to 1/608400 (6-places) and 2/23409 (4-places), respectively.

The square root of 3 is an irrational number. It is also known as Theodorus' constant, named after Theodorus of Cyrene.

It can be expressed as the continued fraction (sequence A040001 in OEIS), expanded on the right.

It can also be expressed by generalized continued fractions such as

which is evaluated at every second term.

Read more about Square Root Of 3:  Proof of Irrationality, Geometry and Trigonometry, See Also

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