① √ AB = √ A √ B √ A ≥ 0B ≥ 0 √ This can be used interchangeably. This can be used for simplification at most, such as √ 8 = √ 4 √ 2 = 2 √ 2.

②√a/b=√a÷√b﹙a≥0b﹥0﹚

③√a？ =|a| (actually equal to absolute value) is the key and difficult point of quadratic root.

When a > 0, √a? =a (equal to itself)

When a=0 √a? =0

When a < 0, √a? =-a (equal to its reciprocal)

This knowledge point is the same as the absolute value! ! ! !

④ Denominators are physical and chemical: Denominators cannot have or contain quadratic roots.

(1) When the denominator has only one quadratic root, then the denominator of the numerator is multiplied by the same quadratic root at the same time by using the fractional property. If the denominator is √3, then the numerator denominator is multiplied by √3 at the same time.

⑵ When the denominator contains quadratic root, the denominator is rationalized by the square difference formula. Specific methods, such as: denominator is √5-2 (indicate the difference between √5 and 2). To make the denominator reasonable, the numerator denominator should be multiplied by √ 5+2 (representing the sum of √ 5 and 2).

I don't know if it is what you want.