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Algebra II/Trig Honors Unit 3 Day 6: Solve Radical Equations Objective: To solve radical equations Definition: Radical Equation - ___________________________________________________________ Solving Radical Equations: Step 1: Isolate the radical on one side of the equation Step 2: Raise each side of the equation to the same power to eliminate the radical Square both sides to eliminate square roots; cube both sides to eliminate cube roots Step 3: Solve. Check your answer in the original equation. Example 1: Solve a radical equation Solve. a. 3 2x 7 3 b. x 25 4 Example 2: Solve a radical equation given a function In a hurricane, the mean sustained wind velocity v (in meters per second) is given by v p 6.3 1013 p where p is the air pressure (in millibars) at the center of the hurricane. Estimate the air pressure at the center of a hurricane when the mean sustained wind velocity is 54.5 meters per second. Solving with Rational Exponents - _______________________________________________________ ___________________________________________________________________________________ Example 3: Solve an equation with a rational exponent Solve. a. 4 x 2 3 36 b. x 2 34 1 7 Extraneous Solutions - ________________________________________________________________ ___________________________________________________________________________________ To avoid extraneous solutions, you should always __________________________________________ Example 5: Solve an equation with an extraneous solution Solve a. x 1 7 x 15 b. 10 x 9 x 3 If an equation has two radicals, you may need to ___________________________________________ Example 6: Solve an equation with two radicals Solve a. x 2 1 3 x HW: Page 208 #3-51 (M3), 53 b. x6 2 x2