7 5 Solving Square Root and Other Radical

7. 5 Solving Square Root and Other Radical Equations • I will be able to solve square root equations by isolating the radical and squaring both sides of the equation. • I will be able to solve equations with rational exponents by isolating the rational expression and raising both sides to the inverse of the exponent. • I will be able to solve equations with two rational exponents by raising both sides to a power that turns the rational exponents into whole numbers.

• I will be able to solve square root equations by isolating the radical and squaring both sides of the equation. Isolate the radical Square both sides Check for extraneous answers 2+4 = 6 Yup!

• I will be able to solve equations with rational exponents by isolating the rational expression and raising both sides to the reciprocal of the exponent. Divide by 2 Raise both sides to the reciprocal of the rational exponent Find both solutions x = 125+2 and x = -125 + 2 and x = -123 x = 127 Check for extraneous answers

• I will be able to solve equations with two rational exponents by raising both sides to a power that turns the rational exponents into whole numbers. Put one expression on one side and one on the other side Pick a power that will raise BOTH sides exponents to whole numbers. FOIL and get all terms to one side Factor and solve Check your answer with the calculator. There can be extraneous solutions