The basis for simplifying these formulas is actually one: √a? = | a |, and understand the meaning of absolute value. Generally speaking, you can't go wrong if you pay attention to this. But there are some special cases as follows.

1 。 a*√(- 1/a)

∫ number of roots-1/a > 0,∴a〈0

∴ Original formula = a √ (-a/a? )= a * 1/| a | *√(-a)= a * 1/(-a)√(-a)=-√(-a)

An "implicit condition" is used here, that is, the known formula should be meaningful, and the root number of ∴-1/a >; 0

In addition, "the absolute value of a negative number is its opposite" is also very important.

2. As we all know.

√(-a？ b)=√[a？ (-ab)]=|a|√(-ab)=-a√(-ab)

The condition of this question is

3.xy & lt0, then √(x? y)

By. Xy < 0 means that x and y are a plus sign and a minus sign. According to the number of prescriptions x? Y≥0, and x? ≥0, so there must be y>0, so x must be negative.

Original formula = | x | √ y =-x √ y

It seems that the characteristic of your group of questions is that in addition to simplifying the definition of root number formula and absolute value, the so-called "implicit condition" is particularly important, that is, the number of roots in the known formula must be greater than or equal to 0.