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  2. Square root of 5 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_5

    The approximation ⁠ 161 / 72 ⁠ (≈ 2.23611) for the square root of five can be used. Despite having a denominator of only 72, it differs from the correct value by less than ⁠ 1 / 10,000 ⁠ (approx. 4.3 × 10 −5). As of January 2022, the numerical value in decimal of the square root of 5 has been computed to at least 2,250,000,000,000 ...

  3. Methods of computing square roots - Wikipedia

    en.wikipedia.org/wiki/Methods_of_computing...

    A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...

  4. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 55, or 5 2 (5 squared). In mathematics, a square root of a number x is a number y such that =; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1]

  5. Root mean square - Wikipedia

    en.wikipedia.org/wiki/Root_mean_square

    In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}

  6. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    A square root of a number x is a number r which, when squared, becomes x: =. Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:

  7. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    Taking the positive root, one finds ⁡ = ⁡ = / = /. A geometric way of deriving the sine or cosine of 45° is by considering an isosceles right triangle with leg length 1. Since two of the angles in an isosceles triangle are equal, if the remaining angle is 90° for a right triangle, then the two equal angles are each 45°.

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  9. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins ⁠ 1 / 1 ⁠ , ⁠ 3 / 2 ⁠ , ⁠ 7 / 5 ⁠ , ⁠ 17 / 12 ⁠ , and ⁠ 41 / 29 ⁠ , so the sequence of Pell ...