The square root is a mathematical operation.
Before entering fully into the analysis of the meaning, we must establish that the etymological origin of the mathematical term square root is found in Latin and more precisely in what is the union of two words: radix and quadrum , which can be translated as “of four".
In the field of mathematics , a certain value that must be multiplied by itself (either on one or more occasions) to arrive at a certain figure is called a root . When referring to the square root of a number, it identifies the number that, when multiplied once by itself, results in a first number .
Examples of square root
To cite a particular case as an example: the square root of 16 is equal to 4 since 4 times 4 is equal to 16 . In other words, we can say that if we multiply 4 by itself (4×4), we get the number 16, which is the same as saying that 4 squared gives us 16.
The square root of 9 , on the other hand, is 3 . The explanation of the operation is identical to the previous example: 3×3=9 , that is, 3 squared or 3 multiplied by itself allows us to obtain the number 9. The question “what number multiplied by itself results in 9?” ?” ( "What number when raised to the second power results in 9?" or "What is the square root of 9?" ) gives us the number 3 as an answer.
A historical tour
The question of the so-called square roots was analyzed during the Pythagorean phase , after it was discovered that the square root of two was not rational (because there was no quotient that would allow it to be expressed). As the definition of the square root expanded, mathematicians began to propose the existence of imaginary numbers and complex numbers .
However, there are much older documents that show us how our ancestors also made use of the aforementioned mathematical operations that concern us now. In this sense, it must be emphasized that the Egyptians resorted to them and this can be confirmed in the well-known Papyrus of Ahmes, dated 1650 BC and which was made during the reign of Apophis I.
The root symbol was devised by Christoph Rudolff.
A copy of a document from the 19th century BC is this papyrus cited, also known as the Rhind Papyrus, which is made up of a series of mathematical problems where in addition to the aforementioned roots there are calculations of areas, fractions, trigonometry, rules of three, linear type equations, progressions and even proportional class distributions.
The symbol used to indicate the root was created by Christoph Rudolff in 1525 from the letter r , although with an extension of its stroke to stylize it. Today this symbol allows us to represent the Latin word radix , from which the term root comes.
Properties of the square root
Among the most significant properties that define a square root we have to explain is the fact that what it does is transform rational numbers into algebraic numbers.
Likewise, we cannot ignore the fact that a square root can be carried out in different ways, based on the “objects” it uses to develop. In this way, for example, it can be done with complex numbers, with quaternionic numbers (extension of real numbers) or even with matrices.