Sometimes, either in the setup of a problem or during some manipulation you create these "extraneous" roots. I first encountered them back in algebra (1 or 2, I can't recall). I admit I was very skeptical at first, but gradually it's just something that I came to intuit without complete understanding. I'd like to explain the term clearly, but an adequate definition eludes me. Sometimes you look at something and you just know the answer. In this particular case we're square rooting a bunch of positive numbers - we know the result has to be positive. We probably 'created' the extraneous root when we squared both sides of the equation.


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