When a power is taken on both sides of an equation, the resulting solutions might not check in the original radical equation. These are called extraneous solutions. You must check solutions by substituting in the values into the original equation and verifying that it produces a true statement.
We want to see why it is important to check all solutions to radical equations.
First, a radical equation is an equation where a square root is used.
Now, square roots (and all even roots) have a really cool property.
Because of the law of signs, we have that:
(-2)*(-2) = 4
2*2 = 4
Then the square root of 4 (or any positive number) actually has two solutions:
√4 = ±2
So when solving a radical equation, we may get two solutions, one called the "real" solution (usually for the positive case) and the extraneous solution (for the negative case).
This is because in general math, we assume that:
√4 = 2 and -√4 = -2
This is just notation to make things easier to be read. And this is why we need to find all the solutions, because the first solution we may get can be an extraneous solution and we usually don't want those, or because we actually want the extraneous solution as it can have important information on a given case.
If you want to learn more, you can read:
https://brainly.com/question/9370639
