To bring a multiplier under the sign of a root or to take out it from there is rather widespread operation which often should be carried out for the solution of various tasks.
Instruction
1. To bring a multiplier under the sign of a root, you will need to build it in the same degree, as at the radical's indicator. For example, at a square root the indicator of the radical is equal to two, at a fourth root – to four, at a cubic root – we rub and so on. Any number or expression can be built in degree. However many was multipliers, each of them can be brought under the sign of a root.
2. Build a multiplier in degree. This process can be presented as the work in which all multipliers are identical and equal to initial number, and their quantity same, as well as an exponent. For example, if you build 10 in the 3rd degree to bring under the sign of a cubic root, then it the same, as 10*10*10, that is the multiplier 10 repeats 3 times. The result – in this example it – can be placed 1000 quietly under a pupil of the cubic radical.
3. If you want to take out a multiplier from under the sign of a root, then perform the return operation: take a root from number. You can use the calculator if root degree small, or to spread out number to simple multipliers if it is supposed that it is necessary to make it.
4. To spread out number to simple multipliers, divide it at first into 2 if it is possible to make it totally (that is, as a result it has to turn out whole). If yes, make it. Then look whether it is possible to divide result into 2 again. Do not forget to write down all multipliers. You divide into 2 until it does not stop being possible, that is until the result stops being whole.
5. Further try to divide totally number into 3 until it stops being possible. After 3 you divide into 5, on 7 and so on. Use prime numbers. Sooner or later you receive a prime number as result of division, it also will be the last from multipliers.
6. If some of simple multipliers repeat several times, they can be taken out from under the sign of a root. For example, if among there are two numbers 3, and a root square, then take out 3 from under the sign of the radical. Pay attention that the quantity of identical multipliers has to coincide with the radical's indicator. Only in this case it is possible to take out a multiplier from under the sign. For example, if you have a root of the fifth degree, and the multiplier 2 repeats 5 times, then 2 it is possible to take out from under the radical's badge.
7. In case you need to bring or take out a fractional multiplier under the sign of a root, then you remember that in a common fraction it is necessary to work separately with numerator and with a denominator. At first take care of that the whole part of fraction was transferred to numerator. For example, 1½ it has to be transformed to a look 3/2.