Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet - Section A-7 Page 3
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9A-59
A-7 Radicals
Properties of Radicals
The process of changing and simplifying radical expressions is aided by the intro-
duction of several properties of radicals that follow directly from exponent prop-
erties considered earlier.
PROPERTIES OF RADICALS
T H E O R E M
For n a natural number greater than 1, and x and y positive real numbers,
1
n
3
n
3
1.
x
x
x
x
n
n
n
5
5
5
2.
xy
x
y
xy
x
y
n
4
n
x
x
4
x
x
3.
n
4
y
y
y
y
E X A M P L E
Simplifying Radicals
2
Simplify.
5
2
5
2
(A)
(3x
y)
3x
y
(B)
10
5
50
25 2
25
2
5 2
3
3
x
x
x
1
3
3
(C)
or
x
3
27
27
3
3
Simplify.
M A T C H E D P R O B L E M
2
2
x
3
7
2
2
7
(A)
(u
v
)
(B)
6
2
(C)
8
In general, properties of radicals can be used to simplify terms raised to
powers, not sums of terms raised to powers. Thus, for x and y positive
C A U T I O N
real numbers,
2
2
2
2
x
y
x
y
x
y
but
2
2
2
x
2xy
y
(x
y)
x
y
Simplifying Radicals
The properties of radicals provide us with the means of changing algebraic expres-
sions containing radicals to a variety of equivalent forms. One form that is often
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