Any arithmetic operation has its opposite.
Addition opposite subtraction, multiplication - division.
They have their "doubles-antipodes" and exponentiation.
Exponentiation assumes that this number should be multiplied by itself a certain amount of time itself. For example, the construction of the number 2 in the fifth degree will be as follows:
2 * 2 * 2 * 2 * 2 = 64.
The number, which must be multiplied by itself,It called the base point and the number of multiplications - its index. Exponentiation correspond to two opposite actions: finding indicator and finding grounds.
Removing the root
Finding the foundation degree is called root extraction. This means that it is necessary to find the number to be raised to the power n, to obtain the.
For example, you must remove the root of the 4th power of the number 16, ie, determine what number should be multiplied by itself 4 times to finally get 16. This number - 2.
This arithmetic operation is recorded with the help of a special sign - the radical: on which the left refers to the power?.
If the exponent is an even number,it may be the root of two numbers with the same module, but with different signs - positive and negative. Thus, in this example it may be of 2 and -2.
The expression must be unambiguous, ie, have one result. To do this, and introduced the concept of arithmetic root, which can only be a positive number. Being less than zero arithmetic can not root.
Thus, in the above example will only arithmetic root number 2, and the second option - -2 - excluded by definition.
To some degree, it is used more often than others, in mathematics there are special names which originally related to the geometry. We are talking about the construction of the second and third degree.
The second degree erect length of the sidesquare, when you need to calculate its area. If you need to find the volume of a cube, its edge length erected in the third degree. Therefore, the second level is called the square of the number, and the third - a cube.
Accordingly, the root is called the second degreesquare and cube root - cubic. Square root - the only one of the roots, the recording of which is not put radical exponent:
? 64 = 8
Thus, the arithmetic of the square root of the number of - a positive number that is necessary to erect a second degree to obtain the number.