Calculation of square roots frightens some school students at first. Let's look how it is necessary to work with them and what to pay attention to. Also we will give their properties.
Instruction
1. About use of the calculator we will not say though, certainly, in many cases it is simply necessary. So, the root X, square from number, is number Y which in a square gives number X. It is necessary to remember one very important point: the root square is calculated only from positive number (we do not take complex). Why? You watch the definition written above. The second important point: the result of extraction of a root if there are no additional conditions, generally is two numbers: + Y and - Y (generally the module Y) as both of them in a square give initial number X that does not contradict definition. A root from zero - zero.
2. Now that, as for concrete examples. For small numbers it is the best of all to remember squares (so and roots - as the return operation) as the multiplication table. I speak about numbers from 1 to 20. It will save your time and to help with assessment of possible value of a required root. So, for example, knowing that a root from 144 = 12, and a root from 13 = 169, it is possible to estimate that the root from number 155 is between 12 and 13. Similar estimates can be applied also to larger numbers, their difference will be only in complexity and time of performance of these operations. Also there is other easy interesting way. Let's show it on an example. Let there is number 16. We learn what number is its root. For this purpose we will consistently subtract from the 16th prime numbers and we will count the number of the executed operations. So, 16-1=15 (1), 15-3=12 (2), 12-5=7 (3), 7-7=0 (4). 4 operations – required number 4. The essence consists in carrying out subtraction until the difference does not become equal 0 or will be just less than the following deductible prime number. Minus of this way consists that thus it is possible to learn only the whole part of a root, but not all its exact value completely, but sometimes to within assessment or an error of calculations and it happens enough.
3. Some main properties: the root from the sum (difference) is not equal to the sum (difference) of roots, and here the root from the work (private) is equal to the work (private) of roots. The root in a square from number X is number X.