101A Simplifying Radicals

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10-1A Simplifying Radicals
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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You have simplified fractions.
answer
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Simplifying Radicals
The simplest form of a radical expression is an
expression that has
No perfect square factors other than 1 in the
radicand.
not simplified
No fractions in the radicand.
not simplified
No radicals in the denominator of a fraction.
not simplified
All radical answers must be in simplified form!
Use the properties of radicals to simplify
radical expressions.
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Product Property of Radicals
Rewrite using a perfect square factor.
Write each factor as a radical.
Simplify.
The problem asked for the positive square root
do not write
An efficient method is to find the largest
perfect square factor.
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Simplify.
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
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Simplify.
Example 1
Example 2
Example 3
Why isnt the answer Because the problem was not

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Simplify.
Example 4
Example 5
Example 6
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Product Property of Radicals
Rewrite using a perfect square factor.
Write each factor as a radical.
Simplify.
Multiply radicals using the product property.
Rewrite as one radical.
Simplify.
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Simplify.
Example 7
Example 8
Example 9
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Simplify a square root with variables.
When finding the principal square root of an
expression containing variables, be sure that the
result is not negative.
It may seem that the answer is
?
What if x has a value of -2.
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Substitute -2 for x in the equation.
For radical expressions where the exponent of the
variable inside the radical is even and the
resulting simplified exponent is odd, you must
use absolute value to ensure nonnegative results.
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Simplify.
Write the problem.
Write the radicand as prime factors.
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Prime factorization is writing a composite number
as a product of its prime factors. You can use a
factor tree to find prime factorizations.
Write the factors in increasing order from left
to right. Use exponents to indicate repeated
factors.
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Simplify.
Write the problem.
Write the radicand as prime factors.
Use product property.
Simplify.
Use good form alphabetical order (inside and
outside of the radical) with radical last.
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Simplify.
Example 11
Example 12
Example 10
Example 14
Example 13
Example 16
Example 15
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Simplify.
Example 11
Example 12
Example 10
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Simplify.
Example 14
Example 13
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Simplify.
Example 16
Example 15
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Homework
10-A2 Pages 532-534 1728,68-70.