MSM07G8_RESBK_Ch04_035-042.pe
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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 Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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 Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston. All rights reserved.
76
38
Holt Mathematics
Holt Mathematics
