Real Numbers And The Pythagorean Theorem Worksheet - Chapter 7 Page 25
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46Approximating a Square Root
2 2
EXAMPLE
—
√
Estimate
71 to the nearest (a) integer and (b) tenth.
a. Make a table of numbers whose squares are close to 71.
Number
7
8
9
10
Square of Number
49
64
81
100
The table shows that 71 is between the perfect squares 64 and 81.
—
√
Because 71 is closer to 64 than to 81,
71 is closer to 8 than to 9.
49
64
71
81
100
7
8
9
10
—
√
71 ≈ 8.
So,
b. Make a table of numbers between 8 and 9 whose squares are
close to 71.
Number
8.3
8.4
8.5
8.6
Square of Number
68.89
70.56
72.25
73.96
Study Tip
—
√
Because 71 is closer to 70.56 than to 72.25,
71 is closer to 8.4
than to 8.5.
You can continue the
process shown in
Example 2 to
68.89
70.56
71
72.25
73.96
approximate square
roots using more
8.3
8.4
8.5
8.6
decimal places.
—
√
71 ≈ 8.4.
So,
Estimate the square root to the nearest (a) integer and (b) tenth.
—
—
—
—
Exercises 20–25
√
√
√
√
5. −
6. −
4.
8
13
24
7.
110
3 3
Comparing Real Numbers
EXAMPLE
—
2
√
—
Which is greater,
5 or 2
?
3
—
√
Estimate
5 to the nearest integer. Then graph the numbers on
a number line.
2
2
2.6
5
2
3
4
2
9
3
—
2
2
√
—
—
2
is to the right of
5 . So, 2
is greater.
3
3
Section 7.4
Approximating Square Roots
311
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education