Do extraneous solutions show up when solving radical equations? If so, explain how we can verify and check the solution to prove whether or not it is extraneous

Extraneous Solutions do exist while solving radical equations.

General Formulas and Concepts:
Alg II
- Solving radical equations

Step-by-Step explanation:
When you solve a radical equation, you always have to check for extraneous solutions. This is because the solution x we found while solving the equation may not work in the original problem.

There are several possible reasons for this. One is the domain of radical functions. We know that on a real number line, we cannot plug in negative numbers under the square root, or we’d get an imaginary number. Another reason is when we square a negative number, it becomes positive.

These are things we must account for when we solve for radical equations. Remember to always check the solutions you found and see if they work. One of them could work, both of them could work, or even neither of them would work.