The main method to determine whether a quadratic radical is the simplest quadratic radical is to follow the definition of the simplest quadratic radical, or to visually observe that the exponent of each factor (or factor) of the radicand is less than the root exponent 2, and the radicand does not contain a denominator. When the radicand is a polynomial, it must be factored before observation.

Example: Which of √8, √18, √32, √2, 3√3, and 5√5 are the simplest quadratic roots?

Answer: √2, 3√3, 5√5 are the simplest quadratic roots.

From the above examples, we can see that when we encounter a quadratic radical, simplifying it will make it easier to solve the problem.

A quadratic radical that satisfies the following two conditions is called the simplest quadratic radical:

(1) The factors of the radicand are integers and the factor is a polynomial;

(2) The number to be squared does not contain any factors or expressions that can be squared.