Learning Objectives
Introduction
Tutorial
In some problems there is only one radical. However, there are some problems that have more than one radical. In these problems make sure you isolate just one.
Step 2: Get rid
of your radical sign.
In other words, if you had a square root, you would have to square it to get rid of it. If you had a cube root, you would have to cube it to get rid of it, and so forth.
You can raise both sides to the 2nd power, 10th power, hundredth power, etc. As long as you do the same thing to both sides of the equation, the two sides will remain equal to each other.
Step 3: If you
still have a radical sign left, repeat steps 1 and 2.
Step 4: Solve the
remaining equation.
If you need a review on solving linear equations, feel free to go to Tutorial 14: Linear Equations in One Variable.
If you need a review on solving quadratic equations, feel free to go to Tutorial 17: Quadratic Equations.
Step 5: Check
for extraneous solutions.
In radical equations, you check for extraneous solutions by plugging
in the values you found back into the original problem. If the left side
does not equal the right side, then you have an extraneous solution.
Example 1: Solve the radical equation .
If you need a review on solving linear equations, feel free to go to Tutorial
14: Linear Equations in One Variable.
*Inverse of mult. by 2 is div. by 2
*True statement
There is one solution to this radical equation: x = 22.
Example 2: Solve the radical equation .
*Square root is by itself on one side of eq.
*Left side is a binomial
squared
If you need a review on solving quadratic equations, feel free to go
to Tutorial 17: Quadratic Equations.
*Use Zero-Product
Principle
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
*False statement
*True statement
There is only one solution to this radical equation: x = 2.
Example 3: Solve the radical equation .
*One square root is by itself on one side of
eq.
*Square root is by itself on one side of eq.
*Inverse of taking the sq. root is squaring
it
*Left side is a binomial
squared
If you need a review on solving quadratic equations, feel free to go
to Tutorial 17: Quadratic Equations.
*Quad. eq. in standard form
*Factor
the trinomial
*Use Zero-Product
Principle
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
*True statement
*True statement
There are two solutions to this radical equation: y = 3 and y = -1.
Solving Equations that have a
Rational Exponent
AND can be written in the form
Step 2: Get rid
of the rational exponent.
For example, if the rational exponent is 2/3, then the inverse operation is to raise both sides to the 3/2 power.
You can raise both sides to ANY power. As long as you do the same thing to both sides of the equation, the two sides will remain equal to each other.
Step 3: Solve the
remaining equation.
If you need a review on solving linear equations, feel free to go to Tutorial 14: Linear Equations in One Variable.
If you need a review on solving quadratic equations, feel free to go to Tutorial 17: Quadratic Equations.
Step 4: Check
for extraneous solutions.
In equations with rational exponents you check for extraneous solutions
by plugging in the values you found back into the original problem. If
the left side does not equal the right side than you have an extraneous
solution.
Example 4: Solve the rational exponent equation .
*Use def.
of rat. exp
If you need a review on solving linear equations, feel free to go to Tutorial
14: Linear Equations in One Variable.
*Inverse of mult. by 3 is div. by 3
*True statement
There is one solution to this rational exponent equation: x = 5.
Example 5: Solve the rational exponent equation .
*Inverse of mult. by 2 is div. by 2
*rat. exp. expression is by itself on one side
of eq.
Also note that it is already solved for x.
So, we do not have to do anything on this step for this example.
*Plugging in 5 to the 3/5 power for x
*True statement
There is one solution to this rational exponent equation: .
Example 6: Solve the rational exponent equation .
*rat. exp. expression is by itself on one side
of eq.
If you need a review on solving quadratic equations, feel free to go
to Tutorial 17: Quadratic Equations.
*Quad. eq. in standard form
*Factor
the trinomial
*Use Zero-Product
Principle
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
*False statement
*False statement
There is no solution to this rational exponent equation.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1b: Solve each radical equation.
Practice Problems 2a - 2b: Solve each rational exponent equation.
Need Extra Help on these Topics?
http://www.sosmath.com/algebra/solve/solve0/solve0.html#radical
Problems 1,2, 3, & 4 of this part of the webpage helps you with
solving equations with radicals. ONLY do
problems 1, 2, 3, & 4.
Go to Get Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for some
more suggestions.
Videos at this site were created and produced by Kim Seward and Virginia Williams Trice.
Last revised on Dec. 16, 2009 by Kim Seward.
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