10-1A Simplifying Radicals
Algebra 1 Glencoe McGraw-Hill Linda Stamper
105
You have simplified fractions.
answer
21
Simplifying Radicals
The simplest form of a radical expression is an expression that has:
No perfect square factors other than 1 in the radicand.
20
259
not simplified
No fractions in the radicand.
not simplified
No radicals in the denominator of a fraction. 2
1not simplified
Use the properties of radicals to simplify radical expressions.All radical
answers must be in simplified
form!
Product Property of Radicals
.0b and 0a where baab
20
54
52
Rewrite using a perfect square factor.
48316
54
316
34
48
34316344
124
An efficient method is to find the
largest perfect square factor.
Write each factor as a radical.
Simplify.
Simplify.
98
Example 1
Example 2
Example 363 40
180
Example 4
Example 5
Example 6150 52
Simplify.
98 249
249
27
Why isn’t the answer Because the problem was not
? 27
. 98
Example 1
Example 2
Example 363 79
79
73
40 104
104
102
Simplify.
180 209
549
56
Example 4
Example 5
Example 6150 625
625
65
52 134
134
132
549
523
Product Property of Radicals
.0b and 0a where baab
20
54
52
Rewrite using a perfect square factor.
54
Write each factor as a radical.
Simplify.
Multiply radicals using the product property.
.0b and 0a where ab ba 322 322
648
Rewrite as one radical.Simplify.
Simplify.
153 153
53
Example 7
Example 8
Example 986 86
48
34
63104 61034 6012
1524
4559 316 15412
15212
Simplify a square root with variables.
2x x
When finding the principal square root of an expression containing variables, be sure that the result is not negative.
22 2It may seem that the answer is…What if x has a value of -2.
22 Substitute -2 for x in the equation.
?
For radical expressions where the exponent of the variable inside the radical is eveneven and the resulting simplified exponent is oddodd, you must use absolute value to ensure nonnegative results.
2x x 4x2x
3xxx
12 xx 5x
xx2
14 xx 22 xx
4 2?
zzyyyxx52 222222
Simplify.
354 zyx20
Write the radicand as prime factors.
Write the problem.
52 x x ySimplify.
y y z z
Use good form – alphabetical order (inside
and outside of the radical) with
radical last.
zzyyx52 22
yz5zyx2 22
If the power of the variable is
an odd number, write the
variable with absolute value
bars
222 yx63
Simplify.
22yx54You can have more than one variable in absolute value bars.
6xy3
Simplify.
24yx81
Example 10
Example 11
Example 1224ba24 yx100 6
Simplify.
24yx81
Example 10
Example 11
Example 1224ba24
2222 baa62
yx100 6
yxxx10 2222
yx9 2 ba62 2
6ba2 2
yx10 3
2222 yxx9
10-A2 Pages 532-534 #17–28,68-70.
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