A radical equation is one that starts out with a square root, cube root, or some other root and gets changed into another form to make the solving process easier. A rational equation is one that involves a fractional expression — usually with a polynomial in the numerator and denominator. Avoid these mistakes when working with radical or rational equations:

  • Forgetting to check for extraneous solutions

  • Squaring a binomial incorrectly when squaring both sides to get rid of the radical

  • Distributing correctly when writing equivalent fractions using a common denominator

  • Eliminating solutions that create a 0 in the denominator