Using restrictions to accept or reject solutions of radical equations

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original equation. We propose alternative solution procedures that are rigorous and simple to execute where the extraneous solutions can be identified without verification against the original equation.

For the slides, go to:
https://faculty.utrgv.edu/eleftherios.gkioulekas/presentations/2021-radical-equations.html

The corresponding research publications are:

E. Gkioulekas: "Using restrictions to accept or reject solutions of radical equations", International Journal of Mathematical Education in Science and Technology 49 (2018), 1278-1292
https://faculty.utrgv.edu/eleftherios.gkioulekas/papers/025-radical-equations-depth-one.pdf
https://doi.org/10.1080/0020739X.2018.1458341

E. Gkioulekas: "Solving parametric radical equations with depth 2 rigorously using the restriction set method", International Journal of Mathematical Education in Science and Technology 51 (2020), 1255-1277
https://faculty.utrgv.edu/eleftherios.gkioulekas/papers/submitted/parametric-rad-equations-depth-two.pdf
https://doi.org/10.1080/0020739X.2020.1807066