the main method to determine whether a quadratic radical is the simplest quadratic radical is based on the definition of the simplest quadratic radical, or by visually observing that the exponent of each factor (or factor) of the radicand is less than the root exponent 2. and the radicand number does not contain a denominator. when the radicand number is a polynomial, it must be factored first and then observed.

example: which of √8, √18, √32, √2, 3√3, and 5√5 are the simplest quadratic radicals?

answer: √2, 3√3 and 5√5 are the simplest quadratic radicals.

as can be seen from the above example, when you encounter a quadratic radical, simplifying it will bring convenience 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 number are integers and the factors are integers;

(2) the radicand number does not contain factors or factors that can solve all squares.