Properties of roots

This article will deal with mathematical expressions. We learn how to extract a root from a number. And for this we shall consider the very concept of the root and the properties of roots.

Definition of the root

If an algebraic expression contains an operationextracting the root, then it is called irrational. The root of any degree of a is the number b, when erected to this degree, we obtain a. N is the index of the root, it can be a natural number that is greater than or equal to 0. A is a number or a root expression.

The action by which the root of a given number is calculated is called the extraction of a root of a power from a. The result of extracting the root is called a radical.

Properties of roots

If we consider the root in the set of real numbers, then we can distinguish the following positions:

1. Two values ​​will have a root of even degree. They will be on the opposite sign in absolute terms equal.
2. The root of an even power of a negative number does not exist.
3. 1 the value will have a root of odd degree of positive number. It will be positive.
4. The root of an odd degree of a negative number will have 1 value, negative.
5. The root of zero is always zero.

With respect to extracting a root of even degree, the set of real numbers is not closed. The result of this action is ambiguous.

With regard to the extraction of an odd-degree root, the set of real numbers is closed. The result of this action is unambiguous.

Properties of the square root

1. If the numbers a and b are greater than or equal to zero, then the square root of the product of such numbers is equal to the product of the square roots of each number separately.
2. If the numbers a and b are greater than or equal to zero, then the square root of the particular such numbers is equal to the quotient of the square roots of each number separately.
3. If the number a is greater than or equal to zero, then the square root of a in degree n is equal to the square root of a in the power of n.