## Solve Rational and Radical Equations

#### Aligned To Common Core Standard:

**High School** - HSA-REI.A.2

How to Solve Radical Equations - Till now, you have learned many mathematical concepts involving square and cube roots. It means that you probably wonâ€™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.

### Printable Worksheets And Lessons

- 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.

#### 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.