Download Lecture Notes for Section 8.5 (More Simplifying and Operations with

Elementary Algebra Notes
Section 8.5
Page 1 of 2
Section 8.5: More Simplifying and Operations with Radicals
Big Idea: It is customary with rational expressions to not have radicals in the denominator. To “get rid of” a
sum of square roots in the denominator, multiply top and bottom by the conjugate of the denominator.
Criteria for a Simplified Radical Expression:

There are as few radicals in the expression as possible.

The radicands are as small as possible.

The radicand has no fractions.

No denominator contains a radical.
To multiply radical expressions with terms, use the distributive property.
Examples:


3
5 42 5  4 5 2 5 5


6  5 2 6  3 5  3 6  2 6  3 6 3 5  5  2 6  5 3 5
 4 5  2 10
 6 6 6 9 6 5 2 5 6 3 5 5
 20  4 5
 6  6  9 30  2 30  3  5
 36  7 30  15
 21  7 30
Practice: Simplify the following radical expressions as much as possible.
1.
2 8  20 


2.

2 5 3
3.

5 3 



32 2 
2
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
4.

2 5 3

Section 8.5
Page 2 of 2

2 5 3 
Rationalizing a denominator with two (square root) terms:
Multiply top and bottom by the conjugate of the denominator so that the denominator becomes a difference of
squares.
Practice: Simplify the following radical expressions as much as possible.
3
5.

2 5
6.
5 3

2 5
7.
5 3  15

10
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.