In order to remove radicals in an equation, we use the principle of powers
and raise both sides to a power which is the same as the index of the
radical. 

If that power is even, we might end up with solutions that do not work since
raising each side to an even will make the signs of each side positive, which
may not be true of the original equation  Often a positive expression
on one side of an equation will equal to a negative expression on the other
side.

However, if that power is odd, we do not need to check,  since raising each
side to an odd will not change the signs of the sides.   

Therefore the problem should be stated:

It is necessary to check the possible solutions when the principle of powers 
is used to solve an equation ONLY when the power is EVEN.

Edwin