IV. Conditions for a simplified expression --it has no negative exponents --it has no fractional exponents in denominator --it is not a complex fraction --the index of any remaining radical is small as possible ***if the original problem is in radical form, the answer should be in radical form *** ***If the problem is in rational exponent form, the answer should be in rational form ***
5.8 R ATIONAL EXPRESSIONS I. Definitions: 1. Radical equations is an equation that has a variable in a radicand. Ex: Not: 2. Extraneous solutions is a solution that does not satisfy the original equation. You can only determine if a solution is extraneous by checking your answer.
II. Steps to Solving Radical Equations: A. Isolate the radical if possible. B. To eliminate the radical, raise each side of the equation to a power equal to the index of the radical. C. Solve the resulting equation. D. Check for extraneous solutions.
VI.Steps to Solving Radical Inequalities A. If the index of the root is even, identify the values of the variable for which the radicand is nonnegative. B. Solve the inequality algebraically. C. Test values to check your solution.