It is necessary to take out from under a root one of factors in situations when it is necessary to simplify mathematical expression. There are cases when it is impossible to execute the necessary calculations by means of the calculator. For example, if instead of numbers alphabetic references of variables are used.
Instruction
1. Spread out a radicand to simple factors. Look what of factors time how many it is specified in root indicators repeats as much, or it is more. For example, you need to take a cubic root from number and in the fourth degree. In this case the number can be presented as an a*a*a* = and * (a*a*a) = a*a3. To an indicator of a root there will correspond in this case the factor a3. It also needs to be taken out for the sign of the radical.
2. Remember properties of roots. Removal from under the sign of the radical represents the action opposite to exponentiation. That is in this case it is necessary to take a cubic root from that a part of expression which gives in to this operation, in this case it a3 3√a*a3 =a3√a.
3. Check calculations. It is especially important if you act with numbers, but not with the designated letters variable. For example, you need to transform expression 3√120. Having spread out a radicand to simple multipliers, you receive 3√120=3 √ (60*2)=3 √ (30*2*2)=3 √ (15*2*2*2)=3 √ (3*5*2*2*2). From under a root it is possible to take out a factor 2. Expression 23√15 will turn out. Check result. For this purpose it is necessary to bring a multiplier at the roots, previously having built it in the corresponding degree. 23 = 8. Respectively, 23√15 = 3 √ (15*8) = 3√120.
4. For decomposition on simple factors of numbers with a large number of categories use the calculator. It is useful to do it also during the work with roots which indicator more than two. During the work with the designated letters variable it is not so important as exact calculations are not necessary.
5. Use search engines. It is necessary, for example, for search of the greatest whole multiplier which can be taken out from under the sign of the radical. Use the Nigma system. Enter into search engine number and what needs to be made with it. For example, enter expression "120 to factorize". You receive the answer 23 (3*5), that is the same which you achieved by oral calculations in the set example. If you need exact calculation, use the online calculator.