Download Radicals/Trigonometry Topic 1:

1
Radicals/Trigonometry
Topic 1:
I. Simplifying Radicals
You have encountered square roots in previous courses. Square roots ( ), also known
as radicals, indicate the positive or principal square root of a number. The number
inside the square root is referred to as the radicand.
1.
25 = 5 2 = 5
 The number 25 is a perfect square
2.
49 = 7 2 = 7
 The number 49 is a perfect square
3.
144 = 12 = 12
 The number 144 is a perfect square
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Example #1: Simplify each of the following.
a.) 100
b.)
9
c.) 121
d.) 1
The numbers shown above are all perfect squares. There are many other perfect squares,
such as 64, 144, and 400.
When working with radicals, whey can be expressed as entire radicals or as mixed
radicals.
When asked to express your answer in mixed radical in simplest form, you must
• Try to write the number under the square root sign as a product of two numbers.
• Try to get one of these factors to be a perfect square (the largest perfect square
possible will make your calculations easier).
Property #1: a × b = a × b, where a ≥ 0, b ≥ 0
Example #2: Express each of the following as a mixed radical in simplest radical form.
a.)
50
b.)
600
c.)
98
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Practice: Express each of the following as a mixed radical in simplest radical form.
a.)
27
b.) 128
c.)
90
Example #3: Express each mixed radical in simplest radical form.
a.) 4 45
b.) −3 28
c.) 2 80
II. Adding and Subtracting Square Roots
Adding and subtracting radicals is very similar to adding and subtracting algebraic
expressions. With algebra, “like terms” can be added or subtracted. Similarly, “like
radicals” can be added or subtracted.
Example #4: Simplify each expression.
a.) 6 2 + 5 2 − 54 2
c.)
3 − 12 6 + 5 3 + 9
b.)
7 − 4 5 − 11 + 7 + 15 − 14 5
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Practice: Simplify each expression. Leave answers in simplest radical form.
a.) 7 2 − 2 7 + 11 2 − 8 2 + 9
b.) 4 13 − 6 + 7 − 5 13 + 6 − 4
Example #5: Simplify each expression. Leave answers in simplest radical form.
a.)
8 − 12 + 18 + 27
b.) 7 12 − 50 + 2 48 − 6 3
Practice: Simplify each expression. Leave answers in simplest radical form.
a.)
8 − 18 + 32 − 50
c.) 3 125 − 2 63 − 20 − 40 3
e.) 2 45 − 3 11 + 36 − 44 + 20 5 − 1
b.) − 12 − 27 + 48 − 75
d.) 2 8 − 4 27 + 3 32 − 3 75
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RADICALS – Worksheet #1
A. Express each of the following as a mixed radical in simplest radical form.
a.)
20
d.) 125
b.)
32
c.) 12
e.)
28
f.)
200
48
i.)
75
g.)
24
h.)
j.)
45
k.) 10800
l.) 1152
B. Write each mixed radical in simplest radical form.
a.) 2 20
b.) 3 18
c.) 4 300
d.) 6 68
e.) −7 32
f.) 4 216
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RADICALS – Worksheet #2
C. Simplify by adding or subtracting.
a.) 2 5 + 6 5
b.) 7 3 + 3 12
d.) 4 27 − 300
e.) 8 40 − 3 490
c.)
20 + 45
f.) 2 24 + 96
g.) −3 11 − 11 + 6 11
h.) 2 8 + 2
i.) 3 112 − 63 + 2 700
j.) −2 180 + 3 80 − 8 720
k.)
m.)
−
1
5
48 + 32 −
27
4
3
4 125 −
100 2 99
+
− 6 49
2
3
l.)
n.)
3 16 −
1
1
1
80 −
64 +
20
2
4
2
3 27 − 3 81 + 3 75 −
1
36
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