Why is it necessary to check all solutions when solving radical equations?

This is one of the reasons why checking your work is so important—if you do not check your answers by substituting them back into the original equation, you may be introducing extraneous solutions into the problem. ... Squaring both sides may have introduced an extraneous solution

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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.

Step-by-step explanation:

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.