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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 = 5 ⋅ 5, 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. Nested radical - Wikipedia

   en.wikipedia.org/wiki/Nested_radical

   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.

6. Algebraic number - Wikipedia

   en.wikipedia.org/wiki/Algebraic_number

   The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.. An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients.

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