Download Radical Equations SN

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)
3t
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