Lesson 2

Lesson 2: Mixed and Entire Radicals that Include Variables

Focus

When driving in a car and there’s a sign indicating a bump in the road, most people tend to slow down a bit. When the vehicle goes over the bump, the speed at which the vehicle hits the bump, as well as the springs in the car, will have an effect on how much a person moves in his or her seat.

Physicists study things that impact motion, and they have developed a formula to calculate the distance a person will be displaced by the bump and the speed at which the person returns to his or her regular position. And wouldn’t you know—it’s a radical equation.

If a vehicle hits the bump too fast, the person may lift up off of the seat. When this happens, most people aren’t thinking about the equation. The higher the bump and the faster the vehicle is travelling, the more the person will move inside the car.

In this lesson you will apply what you already know about converting between entire radicals and mixed radicals to expressions in which the radicand contains variables. You know that it’s not possible to find the square root of a negative number, so you will need to identify the values of the variables for which the radical expression is defined. Doing so will allow you to better understand and work with radical equations, such as the example of the speed bump and the many other radical expressions that you will encounter in the future.

This lesson will help you answer the following inquiry questions:

• How do you express a mixed radical that includes variables in the radicand as an entire radical?

• How do you express an entire radical with a variable coefficient as a mixed radical?

• How do you identify values of the variable for which the radical expression is defined?

Assessment

• Lesson 2 Assignment

All assessment items you encounter need to be placed in your course folder. You should have already had a discussion with your teacher about which items you will be handing in for marking. For those items that you will not be handing in for marking, you should have already had a discussion with your teacher about how you can access the solutions to these questions. Make sure to follow your teacher’s instructions.

Save a copy of the Lesson 2 Assignment to your course folder.

Materials and Equipment

• calculator