Can a square root be negative? Well, the answer is: it depends on what was printed in the problem. The principal square root symbol never has a negative output, so if the test maker printed that symbol, it’s restrictions have to be respected: all square roots then are positive. On the other hand, if the problem contains a variable squared, or some other algebra that leads to a variable squared, and you yourself take a square root as part of the act of solving, then you always have to consider all possible solutions, both the positive square roots and the negative square roots.

If you master that distinction, you will always understand when to consider both positive and negative roots vs. when to consider only the positive root. You may want to go back to those two QCs at the beginning and think them through again before reading the solutions below.