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Root properties

Oksana Logunova
Oksana Logunova
February 28, 2013
Root properties

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

Root definition

If an algebraic expression contains an operation to extract the root, then it is called irrational. The root of a power in a is the number b, when raised to this power, we get a. N is an indicator of the root, it can be a natural number that is greater than or equal to 0. A is a number or a radical expression.

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

Root properties

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

  1. Two values ​​will have an even root. They will be the opposite sign in absolute value.
  2. A root of an even degree of negative number does not exist.
  3. 1 value will have an odd root of a 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 such an action is ambiguous.

Regarding the extraction of an odd root, the set of real numbers is closed. The result of this action is unambiguous.

Square root properties

  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 quotient of 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 to the power n will be equal to the square root of the number a to the power n.
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