Download WS 2.2

Unit II -- Geo1
Worksheet 2 (pre 9.1)
To simplify square roots, you must first be very familiar with “perfect squares.”
Perfect squares are numbers that have integer square roots.
Let’s complete the perfect square chart:
Perfect Square
The square root of the perfect square
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4
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1
Worksheet 2 (pre 9.1)
Unit II -- Geo1
Simplifying With Square Roots:
To simplify square roots, first check if the number is a perfect square. If it is, then the number
that you multiply by itself to get the perfect square, is your answer. For example,
100 = 10 because 100 is a perfect square and when you multiply 10 by itself you get
100.
If the number is not a perfect square, you look for the highest perfect square that is a factor
of that number and you rewrite the square root as a product of the perfect square and the
other factor. For example, if you want to simplify 72 , the highest perfect square that is a
factor of 72 is 36 so you rewrite the square root to look like this:
36 • 2 . Now, we know that the square root of 36 is 6 so we pull out the 6 out of the
square root and write our answer as follows: 6 2 . Always make sure that the number
inside the square root is completely reduced, meaning there is no perfect square (besides
1) that is a factor of that number!
Simplify the following:
1.
49
5. 6 8
9.
13.
48
18
17. 3 44
2. 3 64
6.
27
10. 78 48
14.
20
18. !5 98
3. !4 625
4.
8
7. !10 27
8.
150
11.
90
12.
456
15.
180
16.
162
19.
48
20. !6 54
Adding and Subtracting With Square Roots:
One can only combine square roots if the roots are the same. These are considered “like”
terms. The root stays the same and the numbers in front of the roots are combined. Make
sure to first simplify the roots and then combine like terms. Example:
!2 72 ! 6 44 + 5 32 First simplify the roots as follows
!2 36 • 2 ! 6 4 •11 + 5 16 • 2 = !12 2 !12 11 + 20 2 = 8 2 !12 11
Simplify the following:
21. 6 13 + 7 13
22. 2 11 ! 8 11
23. 2 12 + 5 3
24. 2 27 ! 4 12
25. 4 8 ! 3 5
26. 8 32 + 4 50
2
Worksheet 2 (pre 9.1)
Unit II -- Geo1
27. 6 20 + 45
28. 6 13 + 7 9
30. 2 48 ! 27
31.
150 ! 2 96
160 ! 360 + 250
33.
29. 2 63 + 8 45 ! 6 28
32. 3 135 ! 2 450
34. 5 32 +
35. 3 1440 ! 2 75 ! 192
28 ! 3 128
36. !2 175 +
243 + 5 63
Multiplying With Square Roots:
To multiply square roots multiply the outside numbers not in the radical and multiply the
inside numbers that are in the radical. Make sure your answer is completely simplified. You
may also choose to simplify the radicals first and then you might have to simplify again after
multiplying. Example: 2 32 • 4 8 First simplify to 8 2 • 8 2 = 64 4 = 64 • 2 =128 .
Notice that when you square a radical, you end up with the number itself without the radical.
Example: 5 3 • 24 = 5 3 • 2 6 = 10 18 = 30 2
Simplify the following:
37. 3 2 • 5 7
2 •5 2
40.
43. ! 2
(
(
2+ 3
)
46. 3 11
)
39.
41.
(
42. !3 !2 5 + 4 6
)
)
(
(
52. 5 2 6 2 ! 3 6
(
)(
(
3!8 5
)
)
55. 3 6 ! 2 3 6 + 2
)
2
59.
(3
48. 7 8 • 3 10
5+ 7
53.
(
5 !2
56.
(
7 + 2 10
14 ! 7
)(
)(
)
(
)
)
)
51. ! 5 3 ! 2 13
5+4
54.
(
57.
(3
2
14 + 2 7
3
)
45. 6 2 • 3 5
47. 5 6 • 2 3
50. ! 3
2
(
2
!3 3
(
49. (!3 10)(! 18)
58.
(!2 3 )(!9 5 )
44. 3 2 5 ! 2
2
(2 5 )
38.
)
60.
x2
)(
7!4
)
7 !1
)(
)
2 !6 3 2!6
61.
x8
Unit II -- Geo1
62.
x9
63.
Worksheet 2 (pre 9.1)
x 11
64.
x 25 y 3
18 x100 y 27
65.
Dividing With Square Roots:
Simplify the following:
66.
70.
1
5
67.
20 500
12 600
2
24
3
2
68.
69.
2 6
8 18
71.
27 51
18 17
72. 3
74.
x2 x
=
21 18
75.
x = 10
78.
5x + 4 = 7
1
1
!9
3
12
Equations:
Solve the following for x:
73.
76.
4 x
=
x 12
3x = 6
77.
2x ! 4 = 8
79. (MCAS 2003)
What is the simplified form of the expression 450 :
a. 15 2
b. 45 2
c. 75 2
d. 225 2
80. (MCAS 2003)
What is the solution to the equation x = 16 ?
81. (MCAS 2001)
Which of the following statments is true:
a. 95 = 10
b. 95 < 10
c.
4
95 > 10
d.
95 < 9