The root of an algebraic expression is any algebraic expression that, raised to a power, reproduces the given expression. The root sign is called a radical below this sign the quantity from which the root is subtracted is placed, therefore called a sub-radical quantity.
It is a mathematical procedure contrary to empowerment, the root of index two is known as the square root. There are also roots of index 3, 4, 5. By means of the empowerment, you can write X3 = 27, to know what number cubed gives As a result of 27, we write ∛27 = 3.
The German mathematician Christoff Rudolff was the one who used the current symbol of the root for the first time, it was a corruption of the Latin word radix which means root and to denote the cubic root Rudolff repeated the sign three times this happened in the year 1525, almost five centuries ago. In one of his first publications with the title "Die Coss" which literally means "the thing", the Arabs called the unknown of an algebraic equation a thing and Leonardo of Pisa also used this name which was later adopted by the Italian algebraists.
Radical expression: it is any indicated root of a number or an algebraic expression. If the indicated root is exact, the expression is rational, otherwise it is exact, it is irrational and the degree of a radical is indicated by its index.
Root signs:
- The odd roots of a quantity have the same sign as the subradical quantity.
- Even roots of a positive quantity have a double sign (±).
Imaginary quantity: the even roots of a negative quantity cannot be extracted because any quantity, positive or negative, raised to an even power generates a positive result as a consequence. These roots are called imaginary quantities therefore the √ (-4) cannot be extracted since the square root of -4 is not 2 because 22 = 4 and not -4.
Square root of integer polynomials: to extract the square root of a polynomial, the following rule of thumb is applied:
- The given polynomial is ordered.
- The square root of its first term is found, which will be the first term of the square root of the polynomial, this root is squared and subtracted from the given polynomial.
- Lower the next two terms of the given polynomial and divide the first of these by the double of the first term of the root. The quotient is the second term of the root, this second term of the root with its own sign is written next to the double of the first term of the root and a binomial is formed, this binomial is multiplied by said second term and the product is subtraction of the two terms that we had lowered.
- The necessary terms are lowered to have three terms, the part of the already found root is doubled and the first term of the already found root is divided and the first term of the remainder is divided by the first of this pair. The quotient is the third term of the root and this is written next to the double of the part of the part of the root found and a trinomial is formed, this trinomial is multiplied by said third term of the root and the product is subtracted from the residue.
- The previous procedure is continued, always dividing the first term of the remainder by the first term of the double of the part of the root found, until obtaining zero remainder.
