Positive real number which when multiplied by itself gives 7
Square root of 7
Rationality
Irrational
Representations
Decimal
2.645751311064590590..._10
Algebraic form
Continued fraction
The rectangle that bounds an equilateral triangle of side 2, or a regular hexagon of side 1, has size square root of 3 by square root of 4, with a diagonal of square root of 7.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
The square root of 7 is the positive real number that, when multiplied by itself, gives the prime number 7. It is more precisely called the principal square root of 7, to distinguish it from the negative number with the same property. This number appears in various geometric and number-theoretic contexts. It can be denoted in surd form as:[1]
and in exponent form as:
It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are:
which can be rounded up to 2.646 to within about 99.99% accuracy (about 1 part in 10000); that is, it differs from the correct value by about 1/4,000. The approximation 127/48 (≈ 2.645833...) is better: despite having a denominator of only 48, it differs from the correct value by less than 1/12,000, or less than one part in 33,000.
More than a million decimal digits of the square root of seven have been published.[3]
^Darby, John (1843). The Practical Arithmetic, with Notes and Demonstrations to the Principal Rules, ... London: Whittaker & Company. p. 172. Retrieved 27 March 2022.
^Sloane, N. J. A. (ed.). "Sequence A010465 (Decimal expansion of square root of 7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Robert Nemiroff; Jerry Bonnell (2008). The square root of 7. Retrieved 25 March 2022 – via gutenberg.org.
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