1. Lesson 1

Mathematics 20-2 M5 Lesson 1

Module 5: Radicals

 

Lesson 1: Mixed and Entire Numerical Radicals

 
Focus
 

This is an artist’s conception of exoplanet Fomalhaut b.

ESA, NASA, and L. Calcada (ESO for STScI)

 

One of the exciting areas of current space research is the search for exoplanets—planets that circle a star outside our solar system. Using new sophisticated technology, scientists have discovered over 500 exoplanets. The image shows an artist’s conception of Fomalhaut b, which is an exoplanet 25 light-years away from Earth.

 

The animation titled “Fomalhaut Orbit Concept” is a simulation of Fomalhaut b’s path around its star. The star is the white dot, Fomalhaut b is the red dot, and the brown ring represents dust and debris. Notice that the planet moves faster when close to the star and slower when farther away.

 

 

This is a screen shot for “Fomalhaut Orbit Concept.”

NASA, ESA, and G. Bacon (STScI)



Many of the equations describing planetary motion involve radicals. One such equation derived from Kepler’s third law is , where

  • T is the time required for one revolution around the star
  • k is the constant for all planets orbiting a particular star
  • R is the planet’s largest distance from its star

Did You Know?

Johannes Kepler was an astronomer who formulated three laws of planetary motion in the early 1600s. If you are interested in learning more about his laws, search the Internet for “Kepler’s laws.”



This is a photograph of a car skidding on a wet road.

© Stephane Bonnel/9272855//Fotolia

Radicals also describe a host of earthly situations, such as the skidding of a car when its brakes are applied on a wet surface or the growth of a wildlife population in an animal study.

 

In this lesson you will refresh some of your knowledge about working with radicals and pick up skills using them. Doing so will allow you to deal with radical expressions and equations that match situations on this planet and throughout the universe.

 

This lesson will help you answer the following inquiry questions:

  • How do you express a mixed radical with a numerical radicand as an entire radical and vice versa?
  • How do you compare and order radical expressions in a given set of mixed and entire radicals?
Time
 

Each module is made up of lessons. Each lesson in Mathematics 20-2 is designed to be completed in approximately 80 minutes. You may find that you require more or less time to complete different lessons depending on your strengths. It is important that you progress at your own pace based on your individual learning requirements.

 

Assessment

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.

 

course folder

 

Save a copy of the Lesson 1 Assignment to your course folder.

 

Materials and Equipment
  • calculator