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Solving Radical Equations
Choose Course
Algebra 2
Radical Functions
Solving Radical Equations
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Solving Radical Equations 1.11 - Solution
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Return to Solving Radical Equations
Solving a
radical equation
usually involves three main steps.
Isolate the radical on one side of the equation.
Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
Solve the resulting equation.
Check the results for
extraneous solutions
.
Now we can analyze the given radical equation.
3
x
+
8
−
6
=
-
3
First, let's isolate the radical,
3
x
+
8
,
on one side of the equation.
3
x
+
8
−
6
=
-
3
AddEqn
LHS
+
6
=
RHS
+
6
3
x
+
8
=
3
We get an isolated radical with index equal to
3
.
Then, we will raise each side of the equation to the power of
3
.
3
x
+
8
=
3
RaiseEqn
LHS
3
=
RHS
3
(
3
x
+
8
)
3
=
3
3
Solve for
x
(
n
a
)
n
=
a
x
+
8
=
3
3
CalcPow
Calculate power
x
+
8
=
2
7
SubEqn
LHS
−
8
=
RHS
−
8
x
=
1
9
Next, we will check for extraneous solutions. We do that by substituting
1
9
for
x
into the original equation. If the substitution produces a true statement, we know that our answer is correct. If it does not, then it is an extraneous solution.
3
x
+
8
−
6
=
-
3
Substitute
x
=
1
9
3
1
9
+
8
−
6
=
?
-
3
Simplify
AddTerms
Add terms
3
2
7
−
6
=
?
-
3
CalcRoot
Calculate root
3
−
6
=
?
-
3
SubTerms
Subtract terms
-
3
=
-
3
✓
Because our substitution produced a true statement, we know that our answer,
x
=
1
9
,
is correct.