Module 5 Summary

 

In this module you observed that many of the laws governing the universe involve the use of radicals. Radical equations can be used to model and predict the behaviour of distant planets. Radical equations can also be used for earthbound things, such as determining the swinging motion of a pendulum and analyzing tire skid marks at the scene of a vehicle collision.

 

In this module you investigated the following inquiry questions:

• What mathematical operations are appropriate for radical expressions?

• How can problems involving radical equations be solved?

In the first few lessons you enhanced your ability to convert back and forth between mixed radicals and entire radicals and to rationalize the denominator in a fractional radical. You expanded your skills at working with radicals by encountering them in binomial and trinomial expressions.

 

The project for this unit involved working with dot paper, drawing straight and tilted squares, and calculating their areas and side lengths. From this understanding, you were able to draw lines of lengths that match radical numbers, such as and . This led to a better understanding that radicals like and are numbers as real and definite as 2 or 5.

 

 

In the last part of the module, you used radical expressions to model and solve real-life situations. Your skills and abilities in working with radical functions expanded as you used them to solve radical equations. You learned that in the process of solving radical equations, you often need to square a radical to remove the radical sign. This may, however, introduce an invalid solution called an extraneous root, so you need to verify each solution by substituting it back into the original equation. Finally, you applied your understanding of solving radical equations to solve a variety of problems.

 

In the next modules you will employ some of the strategies you developed when working with radical expressions and equations.