Log in Register

Login to your account

Username *
Password *
Remember Me

Create an account

Fields marked with an asterisk (*) are required.
Name *
Username *
Password *
Verify password *
Email *
Verify email *

Newsletter

Please select a list in the module configuration!No fields selected! Select at least "email"!

Rationalizing Denominators in Radical Expressions


Introduction

The following problem is an example of simplifying square root of a fraction:

Rat_Denoms_vis_1

This problem seems to have been simplified as much as possible.  However, square roots are irrational numbers and are not permitted to remain in the denominator of a fraction.  Further simplification is called rationalizing the denominator and is required in order to change the fraction into one whose denominator is rational. 

Lesson

Everyone knows that a number divided by itself is equal to 1.  The same is true of a decimal and also of a square root… the square root of a number divided by itself is equal to 1. 

Rat_Denoms_vis_2

This is an important fact because you can multiply an answer by 1 and it remains the answer.  The introduction to this lesson contained a fractional answer that contained an irrational number in the denominator.  You aren’t allowed to leave your final answer in this format, so rationalize the denominator as follows:

Rat_Denoms_vis_3

Rational numbers include all positive and negative whole numbers as well as all terminating decimals.  When dealing with fractions, the denominator will generally be a whole number after rationalizing the denominator (only in an unusual case will the denominator be a decimal after it has been rationalized)

Example 1:  Simplify the fraction Rat_Denoms_vis_4

        Solution: Rat_Denoms_vis_5a

 

Some problems result in an answer that has a radical in the denominator.  In this case, you should automatically continue simplifying by rationalizing the denominator.

Example 2:  Simplify the fraction Rat_Denoms_vis_6

        Solution: Rat_Denoms_vis_7a

 

Example 3:  Simplify the fraction Rat_Denoms_vis_8 

        Solution: Rat_Denoms_vis_9a

 

 When simplifying radical expressions, remember to begin by finding the largest possible perfect square number that is a factor of the number in the radical.  In example 2 (for example), 4 is the perfect square factor of 28 and 25 is the largest perfect square factor of 75.  Once you have identified the largest perfect square factor, simply use the properties of multiplication, division, and square roots to find the final answer. 

Review

Simplify each radical expression:

1)  Rat_Denoms_vis_10a

 2)  Rat_Denoms_vis_11a

3)  Rat_Denoms_vis_12a

4)  Rat_Denoms_vis_13a 

 

Scroll Down for Answers…

 

 

 

 

 

 

 

Answers:

1)  Rat_Denoms_vis_10b

2)  Rat_Denoms_vis_11b

3)  Rat_Denoms_vis_12b

4)  Rat_Denoms_vis_13b

Copyright © 2014. Free Math Resource.
All Rights Reserved.