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Square Multiplication - Calculator
Calculator for the edge lengths of a square, if its area gets multiplied. Please enter for both squares either edge length or area. The other two values will be calculated.
Doubling a square with compass and straightedge is a fundamental construction problem in geometry that, unlike doubling a cube, was successfully solved in ancient times. The construction requires a straight line with the length of the square root of two, which is exactly possible since square roots are among the constructible lengths. This construction method extends to any integer multiplication ratio, as the square root of any natural number, whether two, three, or five, can be derived using compass and straightedge. Quadrupling a square is particularly simple, since the square root of four is two. In this case, the side lengths have simply to be doubled.
Mathematically speaking, every operation with compass and straightedge corresponds to a quadratic equation, which exactly matches the requirement to determine the side length of a square for a given area A using the formula s = √A. While it is impossible to geometrically represent the cube root, the square offers a direct tool for solving it through the Pythagorean theorem. A classic aid for this is the diagonal of the unit square, which yields the length √2. Of course, the problem can also be approached mathematically, as this calculator does. However, the square root of two, being an irrational number, can only be represented by decimal fractions with an arbitrary, but never completely exact, degree of precision. The geometric construction, on the other hand, provides the theoretically exact result.
Last updated on 01/23/2026. Author: Jürgen Kummer
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