Chapter 5 e X P O N e N T S a N D r O O T S 117

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

3.^162222
22

(^3) xy^75333 xxx^33 yy^2333 xxy^333333 xy^2
xxy xy

=^322 = 22 xy^223 xy

4. ()()()()()
   (

41 4141 41 41

41

(^5) xx^8553 xx (^555) x^3
x
−= −−=− −
=−))(^541 x−)^3

5. 25 ()xx+= += += 4545 22 22() ()()xx 4542 +
   6.^4 xy^96 ==^4 xxx^4414 yy^24 xxy^444444 xy^2 ==xxy^4 xy^12 xy^2244 xy


6. x
   y

x

y

xx

yyyy

100

(^50200)
50 100
50 100
50 50 50
== 50 50 50 50 50 =
xxx
yyyy
xx
yyyy
x
y
50 5050 50
50 5050 5050 5050 50
2
== 4
We can use the same radical properties to simplify roots of numbers that are
not perfect squares, cubes, etc. If the number under the root (also called the
radical symbol), n , has a factor that is a perfect power of n, then the radical
can be simplified. For example, 18 be simplified because it has a perfect square
as a factor. We separate the perfect power (in this case, 9) from the other factors
and use root properties. In the following examples, we use the same properties,
nnab= abn and naan= , to simplify quantities such as 18.
EXAMPLES
Simplify the expression.
(^18)
18 has a perfect square, 9, as a factor. We write 18 as the product 9 · 2 and
then use the property nnab= abn to separate 9 from 2 and then the property
naan= to eliminate the radical from 9. Thus, 18 =⋅== 92 9232.
48 == 432243 = 43
(^3162) =⋅⋅= ⋅= (^33332333333236)
(^564) xy^63 =⋅ (^52255) xxyx^3 ==^5225555 xy^322 xx (^5) y^3
(^3) ()()()()() 27 xx−=^532727 −−^32 xx=− (^3) 27 27 27^33 xx−=^2 ( − ))( (^327) x− )^2
48
25
x^3
EXAMPLES
Simplify the expression.
EXAMPLES
Simplify the expression.