The root in mathematics can have two values: this arithmetic action and each of solutions of the equation, algebraic, parametrical, differential or any other.
Instruction
1. A root n-ache degrees from number a - it is such number that if to build it in n-uyu degree, the number will turn out and. The root can have up to two decisions or not have the decision in general. This definition is fair when action is made over a real number, both positive, and negative. In the field of complex numbers the root always has the number of decisions coinciding with its degree.
2. The root from a real number, as well as other arithmetic operations, has several general properties: • Root from zero too zero 0; • Root from unit too unit 1; • The root from the work of two numbers or expressions is equal to the work of roots from these expressions at non-negative sizes; • The root from division of two sizes is equal to the relation of roots from these sizes at the value of a divider not equal to zero; • A root n-ache degrees from number and it is possible to write down in the form of a^(1/n); • A root n-ache degrees from number and, m built in degree, it is possible to write down in the form of a^(m/n); • At capture of a root from a root of number and degree of roots are multiplied, i.e. (a^(1/n)) ^(1/m) = a^(1/mn).• a root of odd degree from a negative number is a negative number; • The root of even degree from a negative number does not exist.
3. At designation of a root the sign √ is used. Degree of a root is written over it, for a square root (second degree) it is not written. The root is called square if its multiplication by itself gives number and.
4. Roots of the equation are elements of a set of solutions of this equation. The decision is such value of an unknown variable at which equality will make sense.