When the variable under the square root is not a square, then what is the general strategy? Any example?
If the variable is a square then
then
then
then
Wrong, I'm afraid:
then
then
then
is correct.
One good reason for using rather than is because then it's obvious what the sign is. is always positive.
You should be able to find all this stuff in a basic primer on calculus: there is invariably a list of "useful" substitutions if the book you're using is worth a damn. If not, then find them on line.