Week 11: Section 8.6: Solving Equations with Radicals
 Objectives:
 Solve radical equations by using the ___________________ ______________________
 Solve radical equations that require ________________ __________________
 Solve radical equations with indexes ______________ ____________ ____________
 Use the power rules to solve a _________________ for a specified _________________
 Objective 1: Solve radical equations by using the power rule
 Power Rule: if both sides of an equation are raised to the ___________ ___________,
all the solutions of the original equation are also solutions of the ______________
_________________
 Example: Solve √
First, we use the ________________ _______________ and ________________
both sides of the equation:
Continue to solve for x below:
x = ______________
We need to check if this is an actual solution or an ___________________ solution
We plug x = 2 back into the ____________________ equation:
So the solution is ________________
 Solving an equation with radicals:
 Step 1: _________________ the radical. Make sure that one radical term is alone on
one side of the equation.
 Step 2: Apply the ________________ ________________. Raise each
_____________ _______________ of the equation to a power that is the same as the
index of the radical.
 Step 3: _________________ the resulting equation. If it still contains a
__________________, repeat steps 1 and 2
 Step 4: ______________ all proposed solutions in the __________________
equation.
 Example: Solve √
Isolate the radical below:
Use the power rule and then continue solving for x below:
So, x = ____________ is the proposed solution
Check this solution below:
So, x = _______ is / is NOT (circle one) a solution
So, x = _______ is an ________________ solution
So, there are ______________ ________________
 Objective 2: Solve radical equations that quire additional steps:
 Example: Solve √
Square both sides and solve below:
Check both solutions below:
Check x = 0:
So, x = 0 is / is NOT (circle one) a solution
Check x = 9:
So, x = 9 is / is NOT (circle one) a solution
So the solution set is _______________
 Example: Solve √
√
We first _________________ one of the radicals:
Now, we use the _____________ ________________ and continue solving below:
So, x = _______________ or x = ____________________
Check both soltuions below:
Check x = 0:
So, x = 0 is / is NOT (circle one) a solution
Check x = 5
So, x = 5 is / is NOT (circle one) a solution
The solution set is _________________
 Objective 3: Solve radical eqautions with indexes greater than 2
 Example: Solve √
√
We use the power rule and raise each side to the______ power below to obtain:
We solve this equation below:
x = _______________ is our proposed solution
Check x = 7:
So, x = 7 is / is NOT (circle one) a solution
The solution set is _____________________
 Objective 4: Use the power rule to solve a formula for a specified variable
 Example: Solve the following formula for a:
√
We assume that x and y act like ____________________
We use the power rule and square both sides below:
_______________ both sides of the equation by ____________ to get:
Continue to solve for a below:
a = ____________________