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11. 1Square Roots
Square Roots
5  25
2
• When we raise a number to the second
power, we have “squared” the number.
• Sometimes we need to find the number
that was squared. That process is called
“finding the square root of a number”.
• Every positive number has both positive
and negative square roots.
Radical
Sign
25  5 and -5
25  5
“Principal” Square Root is the positive 5.
Simplify:
(Answer is only the principal root)
81
 64
9
-8
36
(6)2  -36
(-6)2  -36
Because (9)2 = 81
 25  5
Negative square Root
Not possible
Rational Numbers
• Comes from the word “ratio”
• Any number that can be expressed
as the ratio of two integers
7
7
yes ,
1
1.3
13
yes ,
10
0.3333
1
yes,
3
Irrational Numbers
• Cannot be written as the ratio of two
integers.
• Decimal never ends and does not repeat.
• Examples of irrational numbers:

0.4545
2
25
Identify the number as irrational or rational
6

1
35
36
The square roots of most whole numbers are
irrational. Only the perfect squares (0, 1, 4, 9,
16, 25, 36, etc.) have rational square roots.
Identify the rational number:
A.
48
B.
49
C.
50
D.
51
49  7
Real Numbers: All the rational
and all the Irrational numbers.
-25 is NOT a real number. 52  25
 5
Real Numbers
0
Rational
2
Numbers
9
5
7
Irrational

Numbers
2
 25
Approximate the value of
25  5
36  6
29
29  5.3
Approximate the value of
9 3
16  4
12
12  3.4
Approximate the value of
64  8
81  9
75
75  8.7
Approximate the value of
 45
 36  6
 49  7
 45  6.8
225
Find without a calculator:
100  10
400  20
15
11  121
2
12  144
2
13  169
2
289
Find without a calculator:
100  10
400  20
13 
2
17 
2
17
625
Find without a calculator:
400  20
900  30
21 
2
22 
2
25
Compare and Contrast
2 3
2
2
(2  3)
2
Assignment:
Page 485
(2-32 even, 33-47 all)