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Lesson 3

1. Lesson 3

1.6. Explore 2

Mathematics 20-1 Module 5

Module 5: Radicals

 

Strategies for when the Radical is in the Denominator

 

In Discover, you may have found that the following statements are true:




formula

Add these two equations to your copy of Formula Sheet.

 

In the following two Try This activities you will explore strategies used to simplify or solve a problem when a radical is in the denominator.

 

Try This 2

 

Consider the fractional radical . What could be done to change the expression so there is no longer a radical in the denominator, without changing the value of the expression?

 

Try any ideas that occur to you, and then check your ideas using your calculator to ensure the value of the expression is unchanged. hint

 

Multiplying the Denominator and the Numerator by a Term to Eliminate the Radical

 

This is a play button that opens Rationalizing the Denominator.

As you may have discovered in Try This 2, to rationalize the denominator in an expression you can multiply both the denominator and the numerator by the term that will eliminate the radical from the denominator. Watch Rationalizing the Denominator to see this strategy in action.



Self-Check 1

 

This is a play button that opens Rationalizing Radical Expressions Self-Check.

Practise this strategy in Rationalizing Radical Expressions Self-Check.



Try This 3

 

Consider the fractional radical . What could be done to change the expression so there is no longer a radical in the denominator, without changing the value of the expression?

 

Try the ideas that occur to you, and check using your calculator to ensure the value of the expression is unchanged. hint

Did you recognize that the denominator is one factor for the difference of squares? By what other factor could you multiply for the difference of squares to get rid of the radical in the denominator of the expression?
If you multiply the expression by 1, the value is unchanged. If you multiply the expression by , the value is unchanged because . By what value of m must you multiply to get rid of the radical in the denominator?