Arithmetic actions with roots of various degree can simplify considerably calculations in the physicist and the technician and to make them more exact. At multiplication and division it is more convenient not to take a root from each factor or a dividend and a divider, and at first to perform the necessary operations with radicands and exponents. That calculations turned out exact, it is necessary to conform to certain rules.
It is required to you
- - roots of the set degree;
- - handle;
- - sheet of paper;
- - calculator.
1. Attentively read conditions of a task and analyze data. Pay attention to exponents. From that, different they or identical, the way of action depends. If it is necessary to multiply roots of the same degree, just multiply among themselves radicands. At the same time it is unimportant with how many roots you deal. The exponent at the same time remains to the same. For example, you need to increase square roots from numbers a, b and c. Expression will look so: √a * √ b * √ c = √abc.
2. Division of roots with identical exponents is carried out likewise. Put the sign of a root with the same indicator. Divide one radicand into another. √a: √b= √ a/b. Instead of an and b it is possible to use any numbers or alphabetic references. Over the sign of a root private put the same exponent that at a dividend and a divider.
3. If exponents different, calculations it is necessary to carry out a little differently. Exponents in this case too participate in process. They need to be given to the general indicator approximately the same as it becomes at reduction of simple fractions. If it is necessary for you you will multiply roots with indicators of m and n, then the general indicator will be mn. Respectively, at the first factor it is necessary to build both numbers in n degree. Increase exponents of the radical by this additional multiplier. In the second case increase both indicators by m. Put the sign of the radical with an indicator of mn and multiply radicands, as well as in the first way. Division is carried out similarly.
4. If roots have coefficients, they need to be multiplied or divided separately. Write down result before the sign of a root under which there is a result of multiplication or division of radicands.
5. Very often happens it is necessary to bring one of factors out of a root or on the contrary. For this purpose the number facing the radical degree which is designated by an indicator needs to build in the same and to remove at the roots. For example, 3√2= √ 9*2= √ 18. It is possible to arrive and vice versa, having spread out a radicand to factors. Take a root from that factor from which it can be done, and bring it out of the sign of the radical.