China was able to find a square root in the second century BC. In Babylon, extraction of subradical value used the brought closer method. Later this way was in detail described, including in verses the Ancient Greek scientist Heron Alexandriyski. Slightly below you learn this option of determination of value of a root and not only.
Instruction
1. Besides that extraction of an arithmetic square root, inverse function to exponentiation, it also practical task. The geometrical point of extraction of a root square is a finding of length of the party of a square when its area is known. It is clear, that only the positive number and a radicand can be result of such operation too can be only positive. This restriction for result and for a root works for all arithmetic roots. If to remove it, then the turned-out root is called already algebraic.
2. To take a root means to solve the equation of a type of x^n-a=0 when we conduct about a root square, we consider a special case of this equation of x^2-a=0. It is obvious that the quadratic equation presented here. If we find roots of such equation, then it will be equivalent to extraction of a root square. In a formula for the solution of a quadratic equation it is necessary to take a root square therefore we sweep aside this way, and we choose easier graphic method of the decision. Having constructed a parabola, you will see two roots of the equation in places of crossing of the schedule with abscissa axis. The result of the graphic decision the confidant, but sometimes is enough also this method. Here only one nuance if we speak about a root arithmetic, then only the positive number has to be result of extraction of a root.
3. Other way of determination of values of a square root about what it is mentioned in the first paragraph. We know what number in a radicand. A trial and error method it is found such whole natural number which after squaring remains less radicand, but it suits us only provided that the following natural number in a square is more, than subradical value. Thus, we define the first in the answer to a question what the square root of number is equal to. Further to the found number we add on one tenth, squaring every time new number. As soon as the result appears more value of subradical number, we stop. Required us number - previous in relation to on what we were interrupted. It is similarly possible to find any number of signs after a comma.
4. And, of course, presently the most optimum and easy way of definition of a square root is, to enter a radicand into the calculator, and then to press the sign of a square root. Everything will be solved. Or it is possible to use special tables. Often found square root irrational number, in such cases, usually the answer is defined to the third sign after a comma or less precisely.