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  2. Rationalisation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rationalisation_(mathematics)

    In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated.. If the denominator is a monomial in some radical, say , with k < n, rationalisation consists of multiplying the numerator and the denominator by , and replacing by x (this is allowed, as, by definition, a n th root of x is a number that ...

  3. Conjugate element (field theory) - Wikipedia

    en.wikipedia.org/wiki/Conjugate_element_(field...

    In mathematics, in particular field theory, the conjugate elements or algebraic conjugates of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial p K,α (x) of α over K. Conjugate elements are commonly called conjugates in contexts where this is not ambiguous.

  4. Conjugate (square roots) - Wikipedia

    en.wikipedia.org/wiki/Conjugate_(square_roots)

    As (+) = and (+) + =, the sum and the product of conjugate expressions do not involve the square root anymore. This property is used for removing a square root from a denominator , by multiplying the numerator and the denominator of a fraction by the conjugate of the denominator (see Rationalisation ).

  5. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

  6. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    Likewise, tan ⁠ 3 π / 16 ⁠, tan ⁠ 7 π / 16 ⁠, tan ⁠ 11 π / 16 ⁠, and tan ⁠ 15 π / 16 ⁠ satisfy the irreducible polynomial x 4 − 4x 3 − 6x 2 + 4x + 1 = 0, and so are conjugate algebraic integers. This is the equivalent of angles which, when measured in degrees, have rational numbers. [2] Some but not all irrational ...

  7. No, photo doesn't show migrants leaving NYC before Trump ...

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    No, photo doesn't show migrants leaving NYC before Trump ...

  8. Periodic continued fraction - Wikipedia

    en.wikipedia.org/wiki/Periodic_continued_fraction

    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.

  9. Which other presidents have pardoned relatives? Trump is on ...

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    WASHINGTON − President Joe Biden’s pardon of his son Hunter Biden, who was convicted of federal gun charges and tax evasion, rocked the political world with Republican lawmakers and President ...