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```MSM07G8_RESBK_Ch04_035-042.pe
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1:21 PM
Page 38
Name
Date
LESSON
Class
Reteach
4-5 Squares and Square Roots
A perfect square has two identical factors.
25 5 5 52 or 25 (5) (5) (5)2 then 25 is a perfect square.
Tell if the number is a perfect square.
If yes, write its identical factors.
1. 121
112 or
2
3. 400
112 or
2
2. 200
112 or
2
25
5 and 25
5
Since 52 25 and also (5)2 25,
both 5 and 5 are square roots of 25.
The principal square root of 25 is 5: 25
5
Write the two square roots of each number.
9
4. 81
⫺9
81
25
5. 625
⫺25
625
13
6. 169
169
⫺13
Write the principal square root of each number.
12
7. 144
80
8. 6400
9. 10,00
0
100
5100
3
5(10) 3
50 3
47
Use the principal square root when
evaluating an expression. For the
order of operations, do square root
first, as you would an exponent.
Complete to evaluate each expression.
10. 3144
20
12
3
36
20
20
11. 25
144
13
169
13
16
13
13
26
12.
ᎏ ᎏᎏ
2
25
1
100
100
1
ᎏ ᎏᎏ
2
25
10
ᎏᎏ ᎏ1ᎏ
2
5
2
1
ᎏ2ᎏ
1
2ᎏ2ᎏ
38
Holt Mathematics
Practice B
4-5 Squares and Square Roots
Practice A
4-5 Squares and Square Roots
LESSON
LESSON
Find the two square roots of each number.
Find the two square roots of each number.
1. 16
2. 49
4, 4
5. 100
3. 1
7, 7
1, 1
6. 4
2, 2
8, 8
3
13. 36
10
1
16
64
10
18. 59
2
19.
100
15
17.
20. 381
16. 121
16
5
100
25
3
27
5
18.
5
15. 100
25
30
25
1
4
2
12. 73
48
10
14. 36 36
26
13
4
12, 12
11. 64
36
9
13. 264
10
16. 16
9
5
10. 100
19
7
6
15. 49
4
8. 144
5, 5
Evaluate each expression.
12. 31
5
4
14. 15 25
16
17.
11. 18
2
10, 10
7. 25
11, 11
9. 32
17
10. 7
6
4. 100
7, 7
6. 121
8, 8
Evaluate each expression.
9. 8
1
3. 49
9, 9
5. 64
8. 64
9, 9
2. 81
6, 6
5, 5
7. 81
10, 10
1. 36
4. 25
19.
27
196
49
2
6)
20. 3(144
2
18
The Pyramids of Egypt are often called the first wonder of the world.
This group of pyramids consists of Menkaura, Khufu, and Khafra.
The largest of these is Khufu, sometimes called Cheops. During this
time in history, each monarch had his own pyramid built to bury his
mummified body. Cheops was a king of Egypt in the early 26th
century B.C. His pyramid’s original height is estimated to have been
482 ft. It is now approximately 450 ft. The estimated completion
date of this structure was 2660 B.C.
Switzerland’s flag is a square, unlike
other flags that are rectangular.
21. If the flag of Switzerland has an area
of 81 ft2, what is the length of each of
its sides? (Hint: s A
)
9 ft
21. If the area of the base of Cheops’ pyramid is 570,025 ft2, what is
the length of one of the sides of the ancient structure?
(Hint: s A
)
22. If the lengths of the sides of a
Switzerland flag are 10 ft, what is the
area of the flag? (Hint: A s 2)
755 ft
100 ft2
22. If a replica of the pyramid were built with a base area of
625 in2, what would be the length of each side?
(Hint: s A
)
25 in.
35
Holt Mathematics
LESSON
Find the two square roots of each number.
2. 576
15, 15
5. 400
A perfect square has two identical factors.
3. 361
24, 24
25 5 5 52 or 25 (5) (5) (5)2 then 25 is a perfect square.
4. 625
19, 19
6. 729
7. 1024
25, 25
Tell if the number is a perfect square.
If yes, write its identical factors.
8. 2500
112 or (11)2
1. 121
20, 20
27, 27
32, 32
50, 50
9
1
10.
4
144
1
2
13.
324
81
11.
6
14.
64
12.
100
16. (
144
20 or (20)
64)
96
36
25
5 and 25
5
Write the two square roots of each number.
9
4. 81
7
not a perfect square
The principal square root of 25 is 5: 25
5
7
15. 6(
225 9)
2. 200
2
Since 52 25 and also (5)2 25,
both 5 and 5 are square roots of 25.
4
4
5
196 49
3
4
3
16
2
3. 400
Evaluate each expression.
9.
Holt Mathematics
Reteach
4-5 Squares and Square Roots
Practice C
4-5 Squares and Square Roots
LESSON
1. 225
36
9
81
25
5. 625
13
6. 169
25
625
169
13
Evaluate each expression.
17. 2
4
36
144
18. 676
15
8
Write the principal square root of each number.
19. 49 441
169
11
12
7. 144
41
20. The distance from base to base, home plate included, on a
baseball field is 90 ft. The bases form a square. What is its
area?
8100 ft2
9. 10,00
0
100
5100
3
5(10) 3
50 3
47
Complete to evaluate each expression.
Switzerland’s flag is a square, unlike
other flags that are rectangular.
10. 3144
20
21. Suppose a seamstress is making a
flag that has to have an area less
than 50 square meters. What is the
longest length, to the nearest tenth,
the sides can be?
(Hint: s A
)
12
3
36
20
20
11. 25
144
13
169
13
16
13
13
26
12.
2
25
1
100
100
1
2
25
10
1
2
5
2
1
2
1
7.0 m
80
8. 6400
Use the principal square root when
evaluating an expression. For the
order of operations, do square root
first, as you would an exponent.
22
37