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Download as PDF; Printable version; In other projects Wikidata item; ... Surd may refer to: Mathematics. Surd (mathematics), an unresolved root or sum of roots;
It can be denoted in surd form as . It is an irrational algebraic number. [1] The first sixty significant digits of its decimal expansion are: 2.23606 79774 99789 69640 91736 68731 27623 54406 18359 61152 57242 7089... (sequence A002163 in the OEIS), which can be rounded down to 2.236 to within 99.99% accuracy.
In fact, Galois showed more than this. He also proved that if ζ is a reduced quadratic surd and η is its conjugate, then the continued fractions for ζ and for (−1/η) are both purely periodic, and the repeating block in one of those continued fractions is the mirror image of the repeating block in the other. In symbols we have
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
4) Indices, Surds and Logarithms 4.1 Law of Indices; 4.2 Laws of Surds; 4.3 Laws of Logarithms; 4.4 Applications of Indices, Surds and Logarithms; 5) Progressions 5.1 Arithmetic Progressions; 5.2 Geometric Progressions; 6) Linear Law 6.1 Linear and Non-Linear Relations; 6.2 Linear Law and Non-Linear Relations; 6.3 Applications of Linear Law; 7 ...
Second Regular Session Sixty-eighth General Assembly STATE OF COLORADO PREAMENDED This Unofficial Version Includes Committee Amendments Not Yet Adopted on Second Reading