Lesson 3

Lesson 3: Rationalizing Radical Expressions

Focus

diver on cliff: Photodisc/Thinkstock; diver in air: Brand X Pictures/Thinkstock

Cliff divers at Acapulco, Mexico, leap out from the cliff face and plunge 35 m into a shallow gorge below. That is comparable to diving off a 12-storey building! In the gorge, the water depth varies from 2 m to 5 m, depending on the wave action. Timing a jump is essential.

A formula to calculate the time it takes for the diver to hit the water is . This radical expression is derived from formulas learned in high school physics where t represents time, d represents distance, and a represents the acceleration due to gravity.

In this lesson you will learn to simplify fractional radicals like the one in this example by writing them without a radical in the denominator.

Outcomes

At the end of this lesson you will be able to

• simplify expressions with radical denominators by changing the denominator to a natural number for both monomial and binomial denominators
  
  
• describe the relationship between rationalizing a binomial denominator of a rational expression and the product of the factors of a difference-of-squares expression
  
  
• explain, using examples, that the square root of a number squared refers to the absolute value of that number

Lesson Questions

You will investigate the following questions:

• 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?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 3 Assignment (Download the Lesson 3 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 5 Glossary Terms and Formula Sheet
  
  
• work under Project Connection