Radical equations are equations where you will find a variable or multiple variables under a radical symbol (√). Over the course of these radical equation worksheets students will work on several different methods for determining the variables in a series of algebraic expressions usually found within a radical. Students will apply basic algebraic properties in order to isolate variables and balance the equations. This is a very common starter skill for advanced algebra skills. We encourage you to start with the lessons and then advance to the guided practice worksheets. Once you have confidence with those, advance to the completely independent work. Make sure to check your answer on your own prior to looking at the answer keys. Just plug your variable back into the equation to see if it solves it. These worksheets include a lesson, review, quiz, and practice worksheets to help you teach your students how to solve radical equations. This can be a complicated topic for many students. Start them off by work on the math behind radicals and everything else will fall into place for them and you.
This lesson will walk you through how to solve a basic problem of this type. You will then tackle two problems on your own.
Solve the following problems by isolating each side. You will work on problem like this example: 4 = √(2 + 2x)
You will be given 10 problems to work on that follow a basic structure. Once you get the hang of 1 or 2 of these, it becomes pretty easy to follow and complete. Example: 8 = √(5 + 2x)
Follow the steps to solve this equation: √(x + 8) = 3. This sheet provides you with plenty of opportunities to practice this skill.
Solve the following radical equations and check and score your answers. Example: 6 = √(3 + 4x) 2. This is a good way to see how you are doing.
This is an activity that you want to do as an entire class. It will allow you to see how the class is doing with the skill. Example: 5 = √(x + 15)
This takes you through all the necessary steps needed to solve for variables found within radical equations. Example: √(x + 8) = 3
Solve the following problems by following the process that we already have described for you. Here is an example problem from this worksheet: 4 = √(2 + 2x)
This is the 2nd available quiz. We would suggest using this with slightly more advanced student than the 1st quiz. Example problems include: 6 = √(3 + 4x)
What are Radical Equations?
Simply put, a radical equation is an equation that contains a radical sign somewhere within it. What is a radical? They are square roots denoted by the symbol'√.' They are also referred to as the root. Roots are the exact opposites of exponents. The number contained in the symbol √ is the number that is produced when a quantity is multiplied by itself.
The number written on the left of the √ in a small size is called the degree or an index number. Degree numbers identify the radicals as either a square root, a cube root, or an nth root. The horizontal line of the radical on the right of the degree is called the vinculum. The radicand is the number we need to find the root of.
The degree refers to the number of times a number will multiply to equal the radicand.
Any equation that is below the vinculum is called a radical equation. Similarly, any expression below the vinculum is called a radical expression.
Rules For Solving Them
To solve them you need to know the rules that are related to this kind of math. These rules must be followed to solve these equations correctly.
The answer should be positive if the number under the vinculum is positive. The answer should be negative if the number under the vinculum is negative.
In the case of multiplication and division, If the radical for two numbers being multiplied or divided are the same, the numbers will multiply or divide without any change to the radical.
The number under the vinculum can be split under two similar radicals. To remove a √ symbol, you need to power the radical with the same number as the degree. Finally, the radical is equal to the inverse of the degree number.
The best way to approach determing these variables is to isolate it to one side of the equation and remove the radical.
Example: √(3x + 6) – 6 = 0
To solve this, we first begin to isolate the variable by adding six to both sides.
√(3x + 6) – 6 + 6 = 0 + 6
√(3x + 6) = 6
Then, we remove the √ by squaring both sides
[√(3x + 6)]2 = (6)2
3x + 6 = 36
3x = 36 – 6
3x = 30
x = 10
x = 3
Uses of These Types of Equations
Radicals might seem like another one of those math things that you will never use in life, but that is not true. Radicals are used daily in many different fields. They are used in architecture, finance, engineering, and biology.
In carpentry, they are used to calculate triangles used in constructing buildings. In engineering, electrical engineers often use radicals to find out how much electricity flows in a circuit.
They are also used to better understand the nature of scientific and financial situations. In biology, scientists use them to find standard deviations when calculating statistical data. Real estate agents also use these types of equation to understand the inflation rate of homes in a particular to better understand the rate at which they are increasing in value.
These are just some examples of how valuable this type of math is in the real world. This shows how important it is to learn them.
There are a series of steps that we would encourage students to follow to make the path of solving these much easier and it will also give you a good handle on the process. Start by separating the radical expression that contains a variable. If you have multiples of this try to separate them individually. To just kick the radical to the curb, raise both sides of the equation to the index of the radical. If you have any remaining radicals, just rinse and repeat what we just did. At this point, you should just be dealing simple algebra that you would need to complete and solve for the individual variables. This process should become standard for you after a bit of practice. Use the worksheets found below to get in all the practice that you might need.