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# Solving Radical Equations

Student Learning
Outcome: To solve
the power rule.

Real-World 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

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, 1-73 odd, 77-81 odd

• Page 531, 1-25 odd