The calculation of square roots frightens some schoolchildren in the first time. Let's see how to work with them and what to look for.
Also we give their properties.
We will not talk about the use of the calculator, although, of course, in many cases it is simply necessary.
So, the square root of the number ix is the number of ig, which gives the number X in the square.
One must remember one very importantMoment: the square root is calculated only from a positive number (complex do not take). Why? See the definition written above. The second important point: the result of the extraction of the root, if there are no additional conditions, in general there are two numbers: + yerk and y-ray (in general, the york module), since they both give the original X-number in the square, which does not contradict the definition.
The root from zero is zero.
Now, as for specific examples. For small numbers, squares (and hence roots - as an inverse operation) are best remembered as a multiplication table. I'm talking about numbers from 1 to 20. This will save your time and help in assessing the possible meaning of the root. So, for example, knowing that the root of 144 = 12, and the root of 13 = 169, you can estimate that the root of the number 155 is between 12 and 13. Similar estimates can be applied to larger numbers, their difference will be only in complexity and The time of execution of these operations.
There is another simple and interesting way. Let's show it on an example.
Let there be a number 16. Let's find out which number is its root. To do this, we will consistently subtract 16 prime numbers from 16 and calculate the number of operations performed.
So, 16-1 = 15 (1), 15-3 = 12 (2), 12-5 = 7 (3), 7-7 = 0(4). 4 operations? The required number 4. The bottom line is to do the subtraction until the difference becomes 0 or it will be just less than the next subtrahend prime number.
The downside of this method is thatIn this way, only the whole part of the root can be recognized, but not all of its exact meaning is completely, but sometimes accurate to an estimate or a calculation error and this is sufficient.
Some basic properties: the root of the sum (difference) is not equal to the sum (difference) of the roots, but the root of the product (particular) is equal to the product of (private) roots.
The square root of the number X is the number x itself.