Generally speaking, the algebraic expression in the form of √ā(a≥0) is called quadratic root. When a≥0, √ ā represents the arithmetic square root of a, and when a is less than 0, it is not a quadratic root (in a quadratic equation with one variable, if the root sign is negative, there is no real root).
Concept: The formula √ā(a≥0) is called quadratic radical, and √ā(a≥0) is non-negative.
Multiplication of two algebras with quadratic roots. If their product does not contain quadratic roots, then these two algebras are called mutually rational factors.
In the process of judging the simplest quadratic root, we should pay attention to:
The (1) quadratic root is not the simplest quadratic root as long as it contains fractions or decimals.
(2) If the exponent of the power is greater than or equal to 2, then every factor (or factor) in the quadratic root is not the simplest quadratic root.