Module 5

Many of the laws governing the universe involve the use of radicals. The simplest example of a radical that you are familiar with is the square root. Radicals can model and predict the behaviour of stars and planets. On Earth, radicals can predict the swinging of a pendulum and determine the outcome of a collision by analyzing tire skid marks at the scene.

 

In Module 5 you will learn more about radical functions and how to work mathematically with radicals. You will enhance your ability to convert back and forth between mixed radicals and entire radicals. You will work on how to rationalize the denominator in a fractional radical. Radicals in binomial and trinomial expressions will provide a new twist.

 

Solving radical equations can be used to model real-life situations and solve problems. In this module you will investigate the following question:

• How are radicals used in science to model and analyze various situations?

To investigate this question you will focus on the lessons and questions in the table.

Lesson	Topic	Lesson Questions
1	Mixed and Entire Radicals	How do you convert between a mixed radical with a numerical radicand and an entire radical?
		Why are radicals expressed in different ways?
2	Operations on Radicals	How do you simplify a complex radical by correctly performing addition, subtraction, multiplication, and/or division?
		For what values of the variable is a given radical expression defined?
3	Rationalizing Radical Expressions	How do you simplify a fractional radical by rationalizing the denominator?
		How do you explain the rules for writing positive and negative roots by using examples?
4	Solving Radical Equations	How do you determine the roots of a radical equation algebraically?
		How do you verify that the values determined in solving a radical equation are viable roots of the equation?
5	Modelling Problems with Radicals	How do you solve problems by modelling situations using radical equations?

 

In Module 5 Project: Plan a Planet, you will design and plan your own exoplanet circling a star outside the solar system. You will use radical functions to model the path of the planet and to design some of the planet’s characteristics.