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 number7.
which can be rounded up to 2.646 to within about 99.99% accuracy (about 1 part in 10000).
More than a million decimal digits of the square root of seven have been published.[2]
Rational approximations
Explanation of how to extract the square root of 7 to 7 places and more, from Hawney, 1797
The extraction of decimal-fraction approximations to square roots by various methods has used the square root of 7 as an example or exercise in textbooks, for hundreds of years. Different numbers of digits after the decimal point are shown: 5 in 1773[3] and 1852,[4] 3 in 1835,[5] 6 in 1808,[6] and 7 in 1797.[7]
An extraction by Newton's method (approximately) was illustrated in 1922, concluding that it is 2.646 "to the nearest thousandth".[8]
Geometry
Root rectangles illustrate a construction of the square root of 7 (the diagonal of the root-6 rectangle).
In plane geometry, the square root of 7 can be constructed via a sequence of dynamic rectangles, that is, as the largest diagonal of those rectangles illustrated here.[9][10][11]
The minimal enclosing rectangle of an equilateral triangle of edge length 2 has a diagonal of the square root of 7.[12]
Scan of US dollar bill reverse with root 7 rectangle annotation
On the reverse of the current US one-dollar bill, the "large inner box" has a length-to-width ratio of , and a diagonal of 6.0 inches, to within measurement accuracy.[14]
^George Wentworth; David Eugene Smith; Herbert Druery Harper (1922). Fundamentals of Practical Mathematics. Ginn and Company. p. 113. Retrieved 27 March 2022.
^
Jay Hambidge (1920) [1920]. Dynamic Symmetry: The Greek Vase (Reprint of original Yale University Press ed.). Whitefish, MT: Kessinger Publishing. pp. 19–29. ISBN0-7661-7679-7. Dynamic Symmetry root rectangles.{{cite book}}: ISBN / Date incompatibility (help)
