Beginning Algebra, 11th Edition

OBJECTIVE 3 Write radical expressions with quotients in lowest terms.

Writing a Radical Quotient in Lowest Terms

Write the quotient in lowest terms.

Factor first.

Now divide out the common factor;

= Identity property; lowest terms NOW TRY

23 + 3

4

3

= 1 # 3 = 1

23 + 3

4

=

(^3) A 23 + (^3) B
3142

323 + 9

12

EXAMPLE 5

SECTION 8.5 More Simplifying and Operations with Radicals 527

Don’t simplify yet!

CAUTION An expression like the one in Example 5can be simplified only by

factoring a common factor from the denominator and eachterm of the numerator. For

example, first factor

as to obtain 1 + 225.

(^4) A 1 + (^225) B
4

4 + 825

4

NOW TRY
EXERCISE 5
Write the quotient in lowest
terms.

1226 + 28

20

NOW TRY ANSWER

5.^326 +^7
5

Complete solution available
on the Video Resources on DVD

8.5 EXERCISES

In this exercise set, we assume that variables are such that no negative numbers appear as

radicals in square roots and such that no denominators are zero.

In Exercises 1–4, perform the operations mentally, and write the answers without doing inter-

mediate steps.

Simplify each expression. Use the five guidelines given in this section. See Examples 1–3.

23.A 28 - (^27) BA 28 + (^27) B 24.A 212 - (^211) BA 212 + (^211) B
A^5 -^22 BA^5 +^22 B A^3 -^25 BA^3 +^25 B
A 26 + 1 B^2 A 27 + 2 B^2
A 227 + 3 B^2 A 425 + 5 B^2
A^6 -^211 B
2
A^8 -^27 B
2
A^527 -^223 BA^327 +^423 B A^2210 +^522 BA^3210 -^322 B
A 226 + 3 BA 326 + 7 B A 425 - 2 BA 225 - 4 B
327 A 227 + 425 B 3214 # 22 - 228 726 # 23 - 2218
(^25) A 23 - (^27) B (^27) A 210 + (^23) B (^225) A 325 + (^22) B
225 + 264 2100 - 249 28 # 22 26 # 26