Solving Rational and Radical Equations Worksheets
These are some of your more complex types of equations to work with and manipulate. A rational equation is one that contains a rational expression somewhere in it. Meaning there is a fraction present within it. Your goal with them is to get rid of the denominator of that fraction as soon as possible. Radical equations are those that possess a radical expression. To solve those types of problems, do your best to get that radical expression all by itself and then it is pretty easy to counter them by squaring them. Just remember that what ever you do to one side of the equals sign has to be done on the other side as well. This collection of lessons and worksheets will help you explore how to analyze and evaluate these types of equations.
Aligned Standard: HSA-REI.A.2
- Working with Radicals Step-by-step Lesson- What is the value of the variable that is buried under the radical?
- Guided Lesson - We cover all three major skills that you will see associated with this standard.
- Guided Lesson Explanation - It is funny how a majority of algebra based problem set require combining like terms.
- Practice Worksheet - Start by solving for variables. Mix them into problem sets.
- Matching Worksheet - Match the equations to their outputs.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
These get progressively more challenging.
- Homework 1 - Solve for c. Write your answer as a decimal.
- Homework 2 - We have to solve for a variable, use inverse operations to undo the operations in the equation.
- Homework 3 - We have to solve a rational equation, first clear the fractions, either by finding the cross products or by multiplying both sides by the lowest common denominator (LCD). Then solve for the variable.
Practice Worksheets
I tried to hit this skill from every angle I have ever seen it in.
- Practice 1 - When we square a root, it cancels out. The opposite is true as well.
- Practice 2 - Be sure to gather like terms and to do the same operation to both sides of the equation.
- Practice 3 - We have to check whether this is an extraneous solution.
Math Skill Quizzes
I haven't seen too many sample tests questions on this skill.
- Quiz 1 - Solve for v. Take time to review how to counter square roots before you start here.
- Quiz 2 - Solve for n. When you have a root on both sides of the equals sign, it is actually pretty simple to work with.
- Quiz 3 - Take this to the end. It covers every skill we introduced here.
How to Solve Rational Equations
These are equations that involve at least one fraction that contains a polynomial in both the numerator and denominator. If you find that each side of the equal symbol contains a single rational expression, you can simply cross multiple. There are many instances where this may not apply.
Since we are dealing with essentially fractions, the best way to approach this is to get rid of the denominators and cut them off at the feet, literally. We can do this by determining the least common denominator. When you effectively remove the denominators, you will be left with an equation that is usually in linear or quadratic form. Before you start worrying about what to do with them make sure to simplify everything.
How to Solve Radical Equations
Till now, you have learned many mathematical concepts involving square and cube roots. It means that you probably won’t be new to the use of radicals in mathematics. In simplest terms, a radical is known as the nth root of any number, for example, x. Here n is assumed to be a positive integer.
Any mathematical equation that contains or has a radical expression in it is called a radical equation. To solve a radical equation, you need to have a thorough understanding of applying exponential rules and understanding of basic algebraic principles.
Solve a radical equation with the following steps: Separate the radical expression from the equation with the variable. If the equation has more than one radical expression, isolate only one of them. Raise the equation equal to the index of the radical. If the equation still has a radical expression, repeat the above steps; otherwise, solve the resulting equation. Raising both sides of an equation may result in a solution that does not make the original equation true. Such solutions are referred to as extraneous solutions.