Any arithmetic action has the contrast. To addition subtraction is opposite, to multiplication – division. Exponentiation has "doubles antipodes" and.
Exponentiation assumes that this number needs to be increased by itself a certain number of times. For example, construction of number 2 in the fifth degree will look as follows: 2*2*2*2*2=64.
The number which needs to be multiplied by itself is called the degree basis, and quantity of umnozheniye – its indicator. To exponentiation there correspond two opposite actions: finding of an indicator and finding of the basis.
Extraction of a root
Stay the basis of degree is called extraction of a root. It means that it is necessary to find number which needs to be built in n degree to receive this. For example, it is necessary to take a root of the 4th degree from number 16, i.e. to define what number needs to be increased by itself 4 times as a result to receive 16. This number – 2. Such arithmetic action registers by means of the special sign – the radical: √, over which the exponent is specified at the left.
Arithmetic root
If the exponent is even number, then two numbers with the identical module, but with different signs – positive and negative can appear a root. So, in the given example it can be numbers 2 and-2. Expression has to be unambiguous, i.e. have one result. For this purpose also the concept of an arithmetic root which can represent only positive number was entered. The arithmetic root cannot be less than zero. Thus, in reviewed only number 2 will be higher an example with an arithmetic root, and the second possible answer –-2 – is excluded by definition.
Square root
For some degrees which are used more often than others in mathematics there are special names which are initially connected with geometry. It is about construction in the second and third degrees. In the second degree build length of the party of a square when it is necessary to calculate its area. If it is necessary to find cube volume, length of his edge is built in the third degree. Therefore the second degree is called a number square, and the third – a cube. Respectively, the square root is called square, and a cube root – cubic. A square root – only of roots at which record over the radical the exponent is not put: 64=8itak, the arithmetic square root from this number is a positive number which needs to be built in the second degree to receive this number.