vast array of knowledge, which is a sign of literacy in the first place is the alphabet.Next, in the same "significant" element are the skills of addition, multiplication and adjacent to them, but on the reverse sense, arithmetic subtraction, division.Lessons in the distant childhood school skills are faithfully day and night: TV, newspaper, SMS, invoices for payment.And everywhere we read, write, view, add, subtract, multiply.And tell me, how often do you had in life, removing the roots, except as in the country?For example, such an entertaining task, like, the square root of the number 12345 ... There is life in the old dog?Mastered?Yes, there is nothing easier!Where is my calculator ... And without him, hand to hand, weak?

first clarify what it is - the square root of the number.Generally speaking, "to remove the root of the number" means to execute arithmetic operation opposite exponentiation - that's you and the unity of opposites in the life application.Exponent, say, a square, is multiplying a number by itself, ie, as taught in school X * X = A or other recording X2 = A, and the words - "X squared equals A '.Then the inverse problem is: the square root of A, X is a number that is being erected in the square of the same A.

square root

From school course known arithmetic method of calculating "in a column" to help perform any calculationswith the first four arithmetic operations.Alas ... For square, more square roots of such algorithms do not exist.And in this case, as the square root without a calculator?Based on the determination of the square root of one conclusion - you need to select the result value brute force of numbers, which is close to the square of the value of the radicand.That's all!Do not have time to pass an hour or two, how to calculate, using a well-known method of multiplication in the "bar" every square root.If you have enough skills to do a couple of minutes.Not even very advanced user of the calculator or PC makes it in one fell swoop - progress.

But seriously, the square root is often performed using a method of "artillery fork": first, take the number whose square, roughly corresponds to the radical expression.It is better if "our square" a little less than this expression.Then adjust the number of their own ability, understanding, for example, multiplied by two, and ... again squared.If the result is greater than the number under the radical, consistently correcting the original number, is gradually approaching his "colleague" under the root.As you can see - no calculator, only the ability to be considered "in a column."Of course, there are many scientific and reasoned and optimized algorithms for computing square roots, but for "home use" above the reception gives 100% confidence in the result.

Yes, I almost forgot to confirm its increased literacy, calculate the square root of the previously mentioned number 12345. Make steps:

1. Take intuitively, X = 100.We calculate: X * X = 10000. The intuition at the height - the result is less than 12345.

2. try, too, intuitively, X = 120. Then: X * X = 14400.I again with intuition order - the result of more than 12345.

3. The above received "fork" of 100 and 120. Choose a new number - 110 and 115. Get accordingly 12100 and 13225 - a plug narrowed.

4. Try to "maybe" X = 111.Get the X * X = 12321. This number is close enough to 12345. In accordance with the required accuracy "fit" can continue or stop the results.That's all.As promised - very simple and without a calculator.

quite a bit of history ...

smart enough to use the square roots has Pythagoreans, school pupils and followers of Pythagoras, 800 BCand then "ran" for new discoveries in the field of numbers.And where did that come from?

1. Solution of the problem with removing the root, gives a result in the form of a new class of numbers.They were called irrational, that is to say, "unreasonable" becausethey are not recorded complete number.The most classic example of this kind - the square root of 2. This case corresponds to the calculation of the diagonal of a square with a side equal to 1 - that is, the influence of the school of Pythagoras.It turned out that a triangle with very specific unit size sides the hypotenuse of a size that is expressed by a number, in which "there is no end."So in mathematics appeared irrational numbers.

2. It is known that Down and Out trouble started.It turned out that this mathematical operation provides another trick - taking the square root, we do not know the square of the number, positive or negative, is a radical expression.This uncertainty results from a double-operation and recorded.

study of related problems has become a phenomenon in the area of â€‹â€‹mathematics called the theory of complex variables that have great practical importance in mathematical physics.

Curiously, the designation of the root - a - applied in his "Universal Arithmetic" is the same ubiquitous Newton and modern look exactly recording the root has been known since 1690 the book of the Frenchman Rolle "Manual of algebra."