Download 4,7,10,11,13,19,20,23,25,27,31,36,38a,44,49,51,59,72,73,81,85

7-1 ROOTS AND RADICAL EXPRESSIONS (p. 363-367)
For any real numbers a and b, and any positive integer n, if a n  b, then a is an n th root
of b.
For instance, 32  9, so 3 is a square root of 9.
Also, 33  27, so 3 is a cube root of 27.
Also, 3 4  81, so 3 is a fourth root of 81.
Example: Find all the real roots of the following.
1
.
1. The cube roots of 0.027, -125, and
64
81
.
2. The fourth roots of 625, -0.0016, and
625
Do 1 a and b on p. 364.
A radical sign is used to indicate a root. The number under the radical sign is called the
radicand. The index gives the degree of the root.
When a number has two real roots, the positive root is called the principal root. The
radical sign indicates the principal root.
For instance, 36 means the principal square root of 36, which equals positive 6.
Example: Find each real-number root.
1. 3  1000
2.  81
Do 2 a-c on p. 364.
When x  4, x 2  16  4  x.
However, when x  -4, x 2  16  4  x.
Therefore, when a < 0,
n
a n  a when n is even.
Remember, when the
is used and the index is even, we are trying to find the principal
(positive) root. Absolute value bars are often needed to make sure that the root is
positive. When the index is odd, you do not have to worry about absolute value bars.
Example: Simplify each radical expression.
9x10
1.
2.
3
a 3b9
3.
4
x 16 y 4
Do 3 a-c on p. 365.
Use the formula w 
d3
in Example 4 and do 4c on p. 365. Do not be concerned with
4
the rest of Ex. 4.
Homework p. 366-367: 4,7,10,11,13,19,20,23,25,27,31,36,38a,44,49,51,59,72,73,81,85
38a. K  1.35 L
8  1.35 L
2
 8 

 L
 1.35 
L  35 ft
x2
 2x - 1
4
b
2
x   4
1
2a
2
y  4 - 8 - 1  -5
1
y  ( x  4) 2  5
4
85. y 