How to make a multiplier from under the sign of the root

Lay out radical expression in simple factors. Let's see which of the factors is repeated as many times as indicated in the figures of the root, or more. For example, you need to extract the cubic root of a number and fourth degree. In this case, the number can be represented as a*a*a*a = a*(a*a*a)=a*A3. The index of the root in this case will correspond withthe multiplier A3. And it should be taken out of the radical sign.

Summarize the properties of the roots. The imposition of under the sign of the radical is an action that is the opposite of exponentiation. That is, in this case, it is necessary to extract the cube root of that part of the expression that yields this operation, which in this case is A3 3√a*a3 =a3√a.

Check out the calculations. This is especially important if you are dealing with numbers, not with lettered variables. For example, you need to convert the expression 3√120. Expanding radical expression into a fraction, you get 3√120=3√(60*2)=3√(30*2*2)=3√(15*2*2*2)=3√(3*5*2*2*2). Under root you can make witha multiplier of 2. Will get 23√15. Check the result. To do this, make the multiplier of the root, previously elevating him to the appropriate degree. 23 = 8. Accordingly, 23√15 = 3√(15*8) = 3√120.

For the decomposition into simple factors of numbers with lots of digits use a calculator. It is useful to do with roote, the rate of which is greater than two. When working with variables marked is not so important, since accurate calculations are not needed.

Use the search engines. This is necessary, for example, to find the highest integer multiplier, which can be taken from under the sign of the radical. Use Nigma. In the search engine type the number and what to do with it. For example, enter the expression "120 to factorize". You will receive a response 23 (3*5), that is the same thing that you have achieved through oral calculations in the given example. If you need a precise calculation, use the online calculator.