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1, manual square root
It is necessary to master Newton iteration method or method of bisection method to calculate the square root manually, and Newton iteration method is a relatively simple method. Take the square root of X as an example, deduce the formula: f (x) = x 2 = a, define the initial value x0=a/2, then xn+ 1=(xn+a/xn)/2, and repeat the iteration until it converges. In addition, multiplication algorithm and dichotomy can also be used for accurate calculation.
2. Calculator prescription
Calculator can calculate roots of any size in real time without knowing the specific operation principle, which greatly facilitates people's calculation. When using the calculator to do the square root, just enter the number of square roots and press the corresponding square root key. Some high-end calculators also support multiple square roots, complex square roots and other functions.
3, special prescription processing method
The roots of irrational numbers, such as root number 2 and root number 3, cannot be accurately expressed as finite decimals or fractions, so approximate methods are needed to solve them. Newton iteration method, dichotomy, continued fraction method and Taylor expansion method are commonly used. For the root of imaginary unit I, we need to adopt different methods according to the specific situation, such as algebraic method and trigonometric function method.
4, the use of prescription
Root operation is widely used in science, engineering, finance, life and other fields. , such as solving trigonometric function value, calculating geographical distance, settling interest and determining reasonable price, etc. Common root signs are golden ratio, magnification factor in lens formula, enthalpy in thermodynamics, root mean square value and standard deviation.
5. Expansion of prescription
Square root operation has also been widely used in modern mathematics, involving algebraic geometry, calculus, topology, number theory and many other fields. In addition, with the development of quantum computing and quantum information technology, square root operation has also become one of the important basic operations in quantum computing, which has groundbreaking significance.