We write the positiveor principal square rootof a number with the symbol
called a radical symbol.For example, the positive or principal square root of 25 is
written
The negative square rootof 25 is written
Since the square of any nonzero real number is positive, the square root of a nega-
tive number, such as , is not a real number.
Finding Square RootsFind each square root that is a real number.
(a) since 6 is positive and
(b) , since
(c) , since
(d) since
(e) since
(f ) since the negative sign is outside the radical symbol.
(g) is not a real number, because the negative sign is inside the radical
symbol. No real numbersquared equals
Notice the difference among the square roots in parts (e), (f ), and (g). Part (e) is
the positive or principal square root of 100, part (f ) is the negative square root of 100,
and part (g) is the square root of -100,which is not a real number.
- 100.
- 100
- 100 = -10,
100 =10, 102 =100.
0.16= 0.4, 1 0.4 22 =0.16.
a
3
4
b
2=
9
16
.
B
9
16
=
3
4
0 = 0 02 =0.
36 =6, 62 =36.
EXAMPLE 3
25
- 25 =-5.
25 = 5.
,
26 CHAPTER 1 Review of the Real Number System
CAUTION The symbol is used only for the positivesquare root, except that
0 =0.The symbol - is used for the negative square root.
NOW TRYNOW TRY
EXERCISE 3
Find each square root that is a
real number.
(a) (b)
(c)- 144
B
100
9
- 144
Order of Operations1. Work separately above and below any fraction bar.
2. If grouping symbolssuch as parentheses , brackets ,or absolute
value bars are present, start with the innermost set and work outward.
3. Evaluate all powers, roots,and absolute values.
4. Multiplyor dividein order from left to right.
5. Addor subtractin order from left to right.
| |
1 2 3 4
OBJECTIVE 3 Use the order of operations.To simplify
what should we do first—add 5 and 2 or multiply 2 and 3? When an expression in-
volves more than one operation symbol, we use the following order of operations.
5 + 2 #3,
NOW TRY ANSWERS
- (a) (b)
(c)not a real number
10- (^123)