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Article 11 — Appendix A.29√ or sqrt — square root functionCategory. Mathematics. Abstract. Square root: definition, graph, properties and identities. References. This article is a part of scientific calculator LiL, scientific calculator LiX, scientific calculator LiLc and scientific calculator LiXc products. 1. DefinitionSquare root function is inverse of the power function with power a = 2 x^{2}The square root is denoted with radical symbol: √xSquare root is equivalent to the power of one second: √x ≡ x^{1/2}2. GraphSquare root function defined for nonnegative part of real axis — so, its domain is [0, +∞). Function graph is depicted below — fig. 1. Fig. 1. Graph of the square root function y = √x.Function codomain nonnegative part of the real axis: [0, +∞). 3. IdentitiesTake into account, that because of square root defined only for nonnegative values, and power of two defined everywhere, the order of these two functions makes difference: √x^{2} ≡ x√(x^{2}) ≡ x and as well x ≡ signx √(x^{2})Reciprocal argument: √(1/x) = 1 /√xProduct and ratio of arguments: √(xy) = √x√y√(x/y) = √x /√y Power of argument: √(x^{a}) = √x^{a} ≡ x^{a/2}4. Solution of quadratic equationQuadratic equation ax^{2} + bx + c = 0has roots x = [−b ± √(b^{2} − 4ac)] /(2a)For equation with even coefficient for the first power ax^{2} + 2bx + c = 0 roots have simplified form x = [−b ± √(b^{2} − ac)] /a5. Solution of normalized quadratic equationNormalized quadratic equation x^{2} + bx + c = 0 has roots x = [−b ± √(b^{2} − 4c)] /2And equation with even coefficient for the first power x^{2} + 2bx + c = 0 has the simplest form for its roots x = −b ± √(b^{2} − c)6. SupportSquare root function √ or sqrt is supported in: Square root function of the complex argument √ or sqrt is supported in:
7. How to useTo calculate square root of the number:
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To calculate square root of the current result:
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To calculate square root of the number x in memory:
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