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  2. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    If the result of step 4 does not equal the result of step 5, then the original answer is wrong. If the two results match, then the original answer may be right, though it is not guaranteed to be. Example Assume the calculation 6,338 × 79, manually done, yielded a result of 500,702: Sum the digits of 6,338: (6 + 3 = 9, so count that as 0) + 3 ...

  3. Nested radical - Wikipedia

    en.wikipedia.org/wiki/Nested_radical

    More generally, we find that + + + + is the positive real root of the equation x 3 − x − n = 0 for all n > 0. For n = 1, this root is the plastic ratio ρ, approximately equal to 1.3247. The same procedure also works to get

  4. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit.

  5. Zero-product property - Wikipedia

    en.wikipedia.org/wiki/Zero-product_property

    In other words, the roots of are precisely the roots of together with the roots of . Thus, one can use factorization to find the roots of a polynomial. For example, the polynomial x 3 − 2 x 2 − 5 x + 6 {\displaystyle x^{3}-2x^{2}-5x+6} factorizes as ( x − 3 ) ( x − 1 ) ( x + 2 ) {\displaystyle (x-3)(x-1)(x+2)} ; hence, its roots are ...

  6. Napier's bones - Wikipedia

    en.wikipedia.org/wiki/Napier's_bones

    Napier's bones is a manually operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier.

  7. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.

  8. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9.

  9. Dirichlet character - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_character

    4.3 Products of prime powers. 4.3.1 Examples m = 15, ... 2 is a primitive root mod 3. ... The factorization of the characters mod 24 is