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)

The rounded value of 1.732 is correct to within 0.01% of the actual value. A close fraction is (1.7321 42857...).

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 [1; 1, 2, 1, 2, 1, 2, 1, ...] (sequence A040001), expanded on the right.

It can also be expressed by generalized continued fractions such as

which is [1;1, 2,1, 2,1, 2,1, ...] evaluated at every second term.