Math 154 — Rodriguez
Angel—9.1
Evaluating Square Roots
A. Definition: A square root of the number a is the number b if b2 = a.
Ex:
A square root of 9 is 3 since 32 = 9.
Another square root of 9 is −3 since (−3)2 = 9.
B. To denote the nonnegative square root of a positive number we write
a = b . This is
called the principal square root. The number a is called the radicand. The
the radical sign.
Ex:
9=3
C. If we wanted the negative square root of a number we would write ! a .
D. Examples: Evaluate or state that the expression is not a real number.
1.
0
6.
49
2.
81
7.
36
49
3.
25
8.
10
9.
50
4. ! 25
5.
!25
E. Observations:
positive perfect square =
positive but not a perfect square =
negative number =
Examples: Indicate whether each statement is true or false.
10.
36 is an irrational number.
11.
30 is an irrational number.
12.
is called
! 4 is not a real number.
Ex: ! 9 = !3