Namely: if x? =a, then √a is called the square root of a, and x = √ a. Where a is called the number of prescriptions. Where the positive square root is called the arithmetic square root.
Regarding the concept of quadratic radical, we should pay attention to:
The number of roots can be a number or an algebraic expression. If the root sign is a positive number or 0, its square root is a real number; If the root sign is negative, its square root is imaginary.
According to this definition, 1, 3, 4, 5 and 6 are all radicals.
2、3-x≥0，x+2≠0； X≤3，x≦-2
3、2-x≥0，x≤2；
4, -5 √ 7 =-√ (25× 7) =- 175, -6 √ 5 =-√ (36× 5) =- 180, the latter is smaller.
5、x- 1=0，x+y-2 = 0； x= 1，y = 2-x = 1； x-y=0
6、x-3≥0，3-x≥0； x≥3，x≤3； x=3，y= 1，x-y=2
7. When √50a=√(25×2a)=5√2a and a=2, √50a=5√4= 10.
8. The side length is √2, √ (4× 3) = √ 12, 2 √ 2 = √ 8.
9、x？ +2x+2=(x+ 1)？ + 1=(√23)? + 1=24
10,5× √ (5/24) = √ (5+5/24), denominator is numerator? - 1;
Rule n×√(n/(n? - 1))=√(n+n/(n？ - 1))