How To Take Square Roots

Square root is a term that refers to the multiplication of a number by its same value a number of times, the result is always the same value. That is to say, that having any number and it is decomposed according to the square root, and this is multiplied by itself, the given result is the same number as had at the beginning. It can also be determined by sight because it has a 2 as an index most of the time. On the other hand, in potentiation, the square root is known as the inverse of a number raised to the square and always represented by the number 2. For example, if you have the number X 4, and it is raised to the square as a power, you have to multiply that number 4 as many times as the 2 indicates, then it is obtained that 4 × 4 = 16. Which leads to show that the square root of 16 is 4, because when multiplied by itself, that will be the result. Every positive natural number has 2 square roots. One positive and one negative. Also, in mathematics, it is known as the natural number, to all that can be counted within the elements of a set. Its origin dates from the year 1650, when it was known as radicion.

The square root has or is divided into 3 parts, the radical, a characteristic symbol that indicates that it is a square root, the index, where it is not necessary to place the number 2, because it is inferring that it is a root square. One of the properties that the square root most represents is the fact that it transforms simple natural numbers into algebraic rational numbers.

What do you need to do square roots?

• Books
• Notebook

Instructions for taking square roots

1. To take a square root, it must be done with a few fixed steps and always depending on the number of figures that the radicand has, and depending on this, the figures must be separated into even groups, that is, 2 by 2. Starting with the right.
2. The exact square root of the first group of figures must be calculated, starting from the left.
3. The square of the root obtained is subtracted from the first group of figures that appear in the radicand.
4. Then, the next group of digits of the radicand or is placed, separating from the number that formed the first to the right and dividing what remains by twice the root that was previously taken.
5. In another of the rows of numbers, double the number of the same row must be placed and then, the quotient of what is obtained is placed so that the number obtained is multiplied by said quotient. At the end, the operable quantity of the radicand is subtracted.
6. The quotient obtained is the second digit of the root.
7. The next cipher group is lowered and the previous operations are repeated.
8. At the end, the square root must be tested to see if the result is the same.

Tips for Taking Square Roots

1. The figures on the right must always be separated and not those on the left.
2. After addition, subtraction, multiplication and division, the square root is the most studied function in school and the most difficult for students to understand.
3. It is necessary to solve operations of the Pythagorean Theorem, proportions and second degree equations, hence the importance.
4. The use of calculators has somewhat minimized the learning of this important basic operation of mathematics, which has somewhat diminished their learning. But the use of this important device should not necessarily be strengthened. It is necessary, at least, to teach the necessary steps for learning the square root.
5. Mental calculation is the basis for being able to solve simple math problems, and this practice can occur in taking the result of simple square roots, so as not to lose the tradition of this important method that has been displaced by the use of the scientific calculator, which brings the built-in square root function.
6. The study and practice of the square root strengthens knowledge about functions, their properties and characteristics.
7. The square root is the inverse operation when squaring any natural number and consists of taking the result of that number when its square is known.
8. The square root is exact as long as the radicand is a number.
9. The square root is integer as long as the radicand is not a perfect square.
10. The integer root of an integer is the largest integer whose square is less than that number.
11. The remainder is the difference between the radicand and the square of the integer root.
12. Every square root of an integer has two signs, positive.
13. In every square root, the radicand is always a positive number or zero.
14. The square root of an integer is that they are always perfect, like everything in mathematics, and if this happens in any problem, it is said to be an irrational number, which does not express anything like the quotient of two integers.
15. Any integer can be expressed as the product of factors raised to an exponent, or what is the same, a base that can be any natural number, the number of times can be multiplied as expressed by the
16. On the other hand, the square root has several uses and functions, among which we can mention calculating the hypotenuse of an equilateral triangle, finding the radius of a circle, if an integer is prime, finding time in uniform motion, to calculate the diagonal of a square, the mean square, the area of ​​an equilateral triangle, obtain the volume of a tetrahedron, define the sine and cosine of a 45º angle, solve second degree equations, among many others.
17. A root is then defined because when the number is multiplied by the number of times indicated by the index, the amount of its radical of the number from which its root is being taken is obtained. It is a complex operation that requires an explanation, step by step to be understood, since it has many gaps in its explanation, which is a little difficult to understand at first, but you have to pay close attention to understand it well.
18. Every root has to do with powers, since the square root can be expressed as a power with a fractional exponent. In addition, the index and the exponent can be simplified together, to reach the smallest expression, although they can also be extended
19. Seeing the roots as a power, it is possible to carry out operations that carry exponents of natural numbers. That is, roots can be multiplied or divided to reduce them to a common index, radicals given 2 numbers can be compared, in addition to expressing the same index of a Positive integer where it is true that 2 or more radicals are equivalent.
20. Given a radical, infinitely many radicals can be obtained, just by multiplying or dividing the exponent of the radicand and the index of the root by the same.