Solving Radical Equations
Student Learning
Outcome: To solve
radical equations using
the power rule.
RealWorld Connection
• You can use radical
equations to solve
problems involving
oceanography and
recreation such as
designing an
amusement park.
DEFINITION
• Radical equation – an equation that has a
__________ in the radicand
• Example:
Connection
• We solve radical equations the __________ way
we’ve solved earlier equations: isolate the
variable, solve and check.
• Refresher:
Solve
3x + 4 = 2x – 6.
3x – 2x = 6 – 4
x = 10
Check:
3(10) + 4 = 2(10) – 6
30 + 4 = 20 – 6
26 = 26
Power Rule for Solving Radical
Equations, page 527
• If both sides of an equation are raised to the
same power, all solutions of the original
equation are also solutions of the new
equation.
• In other words, to “get rid of a radical”,
raise __________ sides to the same
__________ as the index.
Steps for
Solving Radical Equations
1. Isolate the __________. (Get it on one side
of the equation by itself.)
2. Use the power rule to __________ the
radical. (Raise both sides to the “root’s”
power.)
3. Solve.
4. Check. (Very important!)
Getting Started
• Solve each equation. Check your solution.
You try…
Definition
• Extraneous solution – a solution that does not
satisfy the __________ equation
Note: Extraneous solutions can occur when you
square both sides of an equation to create a
new equation. Always check your answers to
be sure none are “extraneous”.
• Special note: If all solutions are
extraneous, the equation has “no
solution”.
See Example 2, page 528.
More Examples
Even More…
ASSIGNMENT
• My Math Lab
• Page 521, 173 odd, 7781 odd
• Page 531, 125 odd
