Calculating square roots scares some students at first. Let's see how to work with them and what to look for.

Also, we give their properties.

instructions

1

About the use of a calculator will not say, though, of course, in many cases it is simply necessary.

So, the square root of the number of X is the number of y, which is the square of the number of X gives.

Be sure to keep in mind one very importantpoint: the square root is calculated only from the positive numbers (complex do not take). Why? See the definition described 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: + y and -igrek (generally a module y), since they are both in a square gives the initial number X, which is consistent with the definition.

The root of zero - zero.

2

Now then, as for specific examples. For small squares of numbers (and therefore the roots - as the inverse operation) it is best to remember how the multiplication table. I'm talking about the numbers from 1 to 20. This will save you time and help in the assessment of the possible values ​​of the desired root. For example, knowing that a root of 144 = 12, and the root of the 13 = 169, we can estimate that the root of the number 155 is between 12 and 13. Similar estimates can also be used for larger numbers, the difference between them is only in the complexity and the time to perform these operations.

There are also other simple fun way. We will show it by example.

Suppose that is the number 16. Learn what the number is a root. To this end, we will consistently be subtracted from 16 prime numbers and count the number of operations performed.

Thus, 16.1 = 15 (1) 15-3 = 12 (2), 12-5 = 7 (3), 7-7 = 0(4). 4 operation? 4. The essence of the desired number is to carry out the subtraction as long as the difference does not become equal to 0 or is less than a subtracted next prime number.

Less of this method is such thatit is possible to learn a whole part of the root, but not all of its exact value completely, but sometimes up to an evaluation or computation errors, and this is enough.

3

Some basic properties: root of the sum (difference) is not equal to the sum (difference) of the root, but the root of the product of (private) is equal to the product of (private) roots.

The root of the square of the number of X is, the number of X itself.