Download Section 10.1

Radical Expressions and Functions - Section 10.1
If a is a nonnegative number, the nonnegative number b such that b 2
square root of a.
The symbol
Examples:
a , is the principal
a, denoted by b
is used to denote the negative square root of a number.
16
4, since 4 2
16
25
5, since
5
2
25
Evaluate the following:
36
64
36
49
81
64
0. 09
9
9
Because each nonnegative real number x has exactly one principal square root, x , there is a square root
function defined by
f x
The domain of this function is 0,
x
(that is, all real numbers greater than or equal to zero).
Fill in the following table and graph the square root function on the axes below.
x f x
0
x
y
3
2
1
1
4
9
0
0
1
2
3
4
5
6
7
8
9
x
1
Let g x
3
2x and find the following values:
g1
g 3
Find the domain of the following functions:
1. f x
x
2. g x
12
3x
3. h x
11x
6
7
For any real number a,
a2
|a|
In words: the principal square root of a 2 is the absolute value of a.
2
Simplify each expression:
2
x
8
49x 10
x2
6x
7
2
9
The cube root of a real number a is written 3 a
3
For example:
3
64
4 since 4 3
a
b means b 3
a
64
3
8
2 since
2
3
8
In contrast to square roots, the cube root of a negative number is a real number. The cube root of a negative
number is negative and the cube root of a positive number is positive.
Because every real number, x, has exactly one cube root, 3 x , there is a cube root function defined by
f x
3
x
Fill in the following table and graph the cube root function.
x
f x
3
x
y
8
2
1
0
3
1
-8
-7
-6
-5
-4
-3
-2
-1
1
-1
1
8
2
3
4
5
6
7
8
x
-2
-3
3
Evaluate the function f x
3
x
5 at the indicated values of x
f 130
f 4
f
22
For any real number a,
3
a3
a
Simplify the following expressions:
3
27x 3
3
64x 15
The nth root of a is denoted n a .
n
For example:
5
32
2 since
5
2
b means b n
a
a
32
4
81
An even root of a negative number is not a real number. For example,
4
3 since 3 4
81
16 is NOT a real number
Evaluate the following:
4
16
5
1
4
6
For any real number a,
Evaluate:
4
x
6
4
n
an
16
1
|a| if n is even
a if n is odd
5
3x
2
5
4