The document discusses squares, square roots, and approximating square roots. It defines a square as a number multiplied by itself and provides examples of perfect squares. It explains that a square root is a number that produces the radicand when squared. Methods are presented for writing radicals, finding square roots, and approximating square roots using the numbers before and after the radicand.

4. • a plane rectangle with and ;
• a four-sided regular polygon

5. • a plane rectangle with and ;
• a four-sided regular polygon

6. • a plane rectangle with and ;
• a four-sided regular polygon
• Has four
equal sides
• A four sided
polygon

7. • a plane rectangle with and ;
• a four-sided regular polygon
2.5 cm
2.5 cm
2.5 cm
2.5 cm

8. • a plane rectangle with and ;
• a four-sided regular polygon
∠𝐴
Has four
equal right
angles

9. • a plane rectangle with and ;
• a four-sided regular polygon
∠𝐴 ∠𝐵
Has four
equal right
angles

10. • a plane rectangle with and ;
• a four-sided regular polygon
∠𝐴 ∠𝐵
∠𝐶
Has four
equal right
angles

11. • a plane rectangle with and ;
• a four-sided regular polygon
∠𝐴 ∠𝐵
∠𝐶∠𝐷
Has four
equal right
angles

12. Point
A of a given
number is a number whose
square is the given number.

13. 1 unit long.
A of a given
number is a number whose
square is the given number.

14. 1 square unit
A of a given
number is a number whose
square is the given number.

15. Example 1:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.

16. Example 1:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.
Its square root is 2.

17. Example 2:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.

18. Example 2:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.
Its square root is 3.

19. Example 2:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.
Its square root is 3.

20. Example 3:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.

21. Example 3:
Find the square root of
this square.
A of a given
number is a number whose
square is the given number.
Its square root is 4.

22. question
s?

24. looks like this when written
Radical Sign
Radicand

25. It is always assumed to be a square root if no number
was present on the index.
2

26. 9 = 𝑠𝑞𝑢𝑎𝑟𝑒 𝑟𝑜𝑜𝑡 𝑜𝑓 9
3
27 = 𝑐𝑢𝑏𝑒 𝑟𝑜𝑜𝑡 𝑜𝑓 27
4
81 = 𝑓𝑜𝑢𝑟𝑡ℎ 𝑟𝑜𝑜𝑡 𝑜𝑓 4
5
243 = 𝑓𝑖𝑓𝑡ℎ 𝑟𝑜𝑜𝑡 𝑜𝑓 243
⋮

27. looks like this when written

28. looks like this when written

29. looks like this when written

30. Notice that -4 is also a square root of 16
because −4 2
= 16. The symbol is
used to .

31. The combination of the radical sign together
with the number is called a .

32. The square root of a does not exist
for there is no real number that will result to that
when squared.

33. question
s?

35. A is a square of a whole
number.

36. Here are the first 20 perfect squares. They are called perfect
squares because they can be arranged into squares.
12 = 1
22 = 4
32 = 9
42 = 16
52
= 25
62
= 36
72
= 49
82 = 64
92
= 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152
= 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400

37. question
s?

39. This is how it looks like if written.
322Base
Exponent

40. And it is read as “3 squared”
322Base
Exponent

41. Power Meaning Verbal Description
42 4 × 4
4 to the second power or
4 squared
73
7 × 7 × 7
7 to the third power or 7
cubed
84 8 × 8 × 8 × 8 8 to the fourth power
95 9 × 9 × 9 × 9 × 9 9 to the fifth power

42. question
s?

43. 2
= 4
Example 1:
2

44. 2
= 9
Example 2:
3

45. 2
= 225
Example 3:
15

46. 2
= 361
Example 4:
19

47. 2
=
1
49
Example 5:
1
7

48. 2
=
1
121
Example 6:
1
11

49. 2
=
81
100
Example 7:
9
10

50. 2
= 82
Example 8:
?

51. question
s?

53. 1.
2
= 49 4.
2
=
1
196
2.
2
= 168 5.
2
=
1
289
3.
2
= 144
Fill in to make each statement true.
7
?
12
1
14
1
17

54. question
s?

55. 9 =
Example 1:
3

56. 64 =
Example 2:
8

57. 49 =
Example 3:
7

58. 169 =
Example 4:
13

59. 225 =
Example 5:
15

60. 484 =
Example 5:
22

61. 576 =
Example 6:
24

62. 1
4
=
Example 7:
1
2

63. 1
81
=
Example 8:
1
9

64. 49
121
=
Example 9:
7
11

65. 0 =
Example 10:
0

66. question
s?

68. 1. 9 = 4. 1
361
=
2. 25 = 5.
3
27 =
3. 324 =
Fill in to make each statement true.
3
5
1
19
3
18

69. question
s?

71. Here’s to follow in approximating square roots.
1. Find the before and just after the number
2. Find the whole number for the approximate square root by
assuming that it is greater than the square root of the before perfect
square by some fraction..
3. Find the denominator by subtracting the perfect square just
after and the perfect square before the number.
4. Find the numerator by subtracting number to be approximated
to the perfect square before it.
5. Change the rational number to decimal.

72. question
s?

73. E-Math 7
Practice and Application
Test V and VI
Page 65