How to make the multiplier under the sign of the root

To make the multiplier under the sign of the root, you will need to elevate it to the same degree as the index of the radical. For example, the square root index of a radical is equal to two, the fourth root – four, the cube root is three, and so on. Any number or expression can be raised to a power. No matter how many multipliers, each of them can be made under the sign of the root.

Raise the multiplier in degree. This process can be thought of as a work in which all multipliers are the same and equal to the original number, and their number is the same as the exponent. For example, if you build 10 3 the degree to make the sign of the cube root is the same as 10*10*10 that is, the multiplier 10 is repeated 3 times. The result in this example is 1000 – you can safely be placed under the pupil of the cubic radical.

If you want to take from under the root sign of the multiplier, then do the reverse action: remove the root of a number. You can use a calculator, if the degree of the root is small, or to decompose the number into Prime factors, if it is assumed that you need to do just that.

To decompose a number into Prime factors, divide it first by 2, if it can be done completely (i.e. the result should be integer). If Yes, do it. Then see if the result is again divided by 2. All the multipliers do not forget to write it down. Divide by 2 until, until it is no longer possible, i.e., until the result ceases to be an integer.

Next, try to divide evenly the number 3 until it is no longer possible. After 3 divide by 5, 7, and so on. Use simple numbers. Sooner or later you will receive as a result of dividing a Prime number, this will be the last of the multipliers.

If any Prime factors are repeated several times, they can be taken from under the sign of the root. For example, if the row has two numbers is 3 and the square root, then take out 3 from under the radical sign. Please note that the number of identical multipliers must match the index of the radical. Only in this case it is possible to make a multiplier out of sign. For example, if you have a fifth root, and multiplier 2 is repeated 5 times, then 2 can be taken from under the radical icon.

If you need to make or give under the sign of the root is a fractional multiplier, remember that fractions need to work separately with the numerator and denominator. First, make sure that the whole part of the fraction was moved to the numerator. For example, 1½ needs to be converted to the form 3/2.