How do you proof ab=ab?

It is not always true. To see the clear picture, we solve some clear examples.
Remember, ab means "find a divided by b then evaluate the square root".
While ab means "find the square roots of a and b first then divide the result".
To proof our case, we will develop four cases, 
Case 1: Let a,bR+ then 
6416=4=2 and 6416=84=2.
These shows that ab=ab is true. 

Case 2: Let aR and bR+ then 6416=4=2i and 6416=8i4=2i.

Case 3: aR+ and bR then 6416=4=2i and 6416=84i=2i therefore, it has failed to hold here, abab?

Case 4: aR and bR then 6416=4=2 and 6416=8i4i=2. Therefore, ab=ab is true.


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