Algebra 1 Honors
1.3 Perfect Squares and Estimation
NOTES
PERFECT SQUARE: This is a number that has a whole number as its square root.
1
Ex:
is a perfect square because 1 is its square root.
4 is a perfect square because 2 is its square root.
2 is NOT a perfect square because it’s square root is approximately 1.4 which is not
a whole number.
Fill in the blanks for the squares and perfect squares given for numbers 1 – 15.
12 = 1
1 =1
92 =
81 =
22 = 4
4
=2
102 =
100
32 =
9
=
112 =
121 =
42 =
16
=
122 =
144
=
52 =
25
=
132 =
169
=
62 =
36
=
142 =
196
=
72 =
49
=
152 =
225
=
82 =
64
=
=
Estimate the following square roots.
**Since these are NOT perfect squares, you are trying to estimate the its decimal value using the
perfect squares you know from above.
a.
27
between
and
215
b.
between
but closer to
but closer to
Estimate:
Estimate:
Square root of a Negative Number:
ex.
and
 36
*What two identical numbers multiply to equal -36?
So…
 36 =
ASSIGNMENT:
In 1 – 16, simplify the perfect squares. If the radical is not a perfect square, write NPS (Not
Perfect Square). If the radical has a negative number under it, write NRS (No Real Solution).
1.
100
2.
64
3.
1
4.
8
5.
9
6.
2
7.
-1
8.
49
9.
25
10.
4
11.
- 16
12.
10
13.
5
14.
144
15.
81
16.
50
In 17 – 22, find the values the square root is between. Use the perfect square below as a
guide. (C Level)
1 1
49  7
16  4
100  10
169  13
4 2
25  5
64  8
121  11
196  14
9 3
36  6
81  9
144  12
225  15
17.
10 is between
and
18.
35 is between
and
19.
55 is between
and
20.
120 is between
and
21.
18 is between
and
22.
200 is between
and
In 23 – 29, estimate the value of the square root to the nearest tenths.
Ex: 24 is between 16 and 25 , so 24 is between 4 and 5. Because 24 is
closer to 25 , the estimate is close to 5. Using the decimals below, since 24 is
almost 25, the estimate has to be very close to 5. So 4.9 is a good estimate!!
16
24
25
4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0
8
23.
52
24.
between
and
Estimate:
30
25.
between
and
between
Estimate:
and
Estimate:
B Level
26.
The estimate decimal value of
a.
b.
c.
d.
28.
27.
The estimate decimal value of
2
2.1
2.8
3
The estimate decimal value of
a.
b.
c.
d.
5
a.
b.
c.
d.
90
8.5
9.1
9.5
10.2
29.
7
7.2
7.7
8
The estimate decimal value of
a.
b.
c.
d.
60
230
15.2
15.7
16.4
16.9
A Level
30. Estimate the follow square root; then explain how
31. Estimate the follow square root; then explain how
you found your answer.
you found your answer.
139 = _________________
150 = _________________
Explanation:
Explanation:
32. Estimate the follow square root; then explain how
33. Estimate the follow square root; then explain how
you found your answer.
you found your answer.
202 = _________________
Explanation:
190 = _________________
Explanation:
1.3 Practice Assessment
Level C
Identify if the statements below
are true or false.
(Circle one)
True
False
7 is between 2 and 3.
True
False
32 is between 5 and 6.
True
False
15 is between 4 and 5.
True
False 83 is between 9 and 10.
True
False
Level B
Which of the following is the best
estimation of
a.
b.
c.
d.
40 ?
Level A
Estimate the follow square root;
then explain how you found your
answer.
7
6
6.3
6.6
164 = _________________
Explanation:
42 is between 7 and 8.
ANSWERS
1. 10
9. 5
17.
9 and 16
25. Approx 5.4
2. 8
10. 2
18.
25 and 36
26. b
3. 1
11. NRS
19.
49 and 64
27. c
4. NPS
12. NPS
20.
100 and 121
28. c
5. 3
13. NPS
21.
16 and
29. a
6. NPS
14. 12
22. 196 and 225
23. Approx 2.8
24. Approx7.2
7. NRS
15. 9
8. 7
16. NPS
Practice Assessment:
1C. true, true, false, true,
false
1B. C
25
33.Approx 13.8
30. Approx. 11.8
31. Approx. 12.3
32. Approx. 14.2
1A. Approx. 12.8