1. Definition: In general, an algebraic expression in the form of √ā(a≥0) is called a quadratic radical. When a > 0, √a represents the arithmetic square root of a, and √0=0.

2. Concept: The formula √ā(a≥0) is called quadratic radical. √ā(a≥0) is non-negative.

Two. Simple properties and geometric significance of quadratic root √.

1)a≥0； √ā≥0[ double nonnegativity]

2) (√ā) 2 = a (a ≥ 0) 【 Any non-negative number can be written as the square of a number 】

3) √ (A 2+B 2) indicates the distance between two points on the plane, that is, the Pythagorean theorem inference.

Three. Properties of quadratic roots and simplest quadratic roots

1) Simplification of Quadratic Radical √ā

a(a≥0)

√ā=|a|={

-a(a