Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Math 20-2 Radicals: Lesson #6 Radical Equations Objective: By the end of the lesson, you should be able to: - Solve a radical equation involving square roots or cube roots - Identify extraneous roots to a radical equation What is the difference between a radical expression and a radical equation? “Solve” means find out what the variable equals. Steps for Solving a Radical Equation 1. Isolate the radical. - move all the numbers outside the radicand to the other side of the equation. 2. Get rid of the root sign by squaring 2 (or cubing 3) both sides of the equation. 3. Solve the resulting equation for x. e.g. 1) Solve the following radical equations. a) 3 4 x 2 c) 5 3x 1 0 b) n 3 12 7 d) 3t 2 6 Math 20-2 Radicals: Lesson #6 Problems: e.g. 2) The formula V PR relates the voltage of an electrical circuit, V volts, to the power, P watts, and the resistance, R ohms. The voltage of a 40-watt amplifier is 80 volts. What is the resistance of the amplifier? e.g. 3) We have seen that the period of a pendulum, T seconds, is related to the length of the L pendulum, L metres by the formula T 2 . If a pendulum completes one full swing 10 in 2.5 seconds, how long is the pendulum, to the nearest hundredth of a metre? e.g. 4) Solve the equation 2 x 9 5 , then check your solution by substituting the answer back into the original equation. What happens? Why? Math 20-2 Radicals: Lesson #6 Key Point: Some radical equations give a solution that doesn’t satisfy the original equation. These are called extraneous roots. * This happens when the isolated square root = a negative number e.g. 5) Which of the following equations have an extraneous root? Solve any that have a solution. a) b) 6 3 y 4 12 c) 3 12 x 2 5x 4 3 Assignment: p. 222-224 #2-3, 6-11, 15 For a challenge: #12-13, 17 More problems: p. 215 #2-4