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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Adding and Subtracting Radicals
8.3
Adding and Subtracting Radicals
Add and subtract radicals.
Simplify radical sums and differences.
Simplify more complicated radical expressions. 1 2 3
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3. Add and subtract radicals.
Objective 1
Add and subtract radicals.
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4. Add and subtract radicals.
We add or subtract radicals by using the distributive property. For example,
Radicands are different
Indexes are different
Only like radicals—those which are multiples of the same root of the same number—can be combined this way. The preceding example shows like radicals. By contrast, examples of unlike radicals are
Note that cannot be simplified.
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5. EXAMPLE 1 Add or subtract, as indicated. Solution:
Adding and Subtracting Like Radicals
Add or subtract, as indicated.
Solution:
It cannot be added by the distributive property.
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6. Simplify radical sums and differences.
Objective 2
Simplify radical sums and
differences.
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7. Simplify radical sums and differences.
Sometimes, one or more radical expressions in a sum
or difference must be simplified. Then, any like
radicals that result can be added or subtracted.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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8. EXAMPLE 2 Add or subtract, as indicated. Solution:
Adding and Subtracting Radicals That Must Be Simplified
Add or subtract, as indicated.
Solution:
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9. Simplify more complicated radical expressions.
Objective 3
Simplify more complicated radical expressions.
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10. Simplify more complicated radical expressions.
When simplifying more complicated radical
expressions, recall the rules for order of operations
from Section 1.2.
A sum or difference of radicals can be simplified only if the radicals are like radicals. Thus, cannot be simplified further.
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11. Simplifying Radical Expressions
EXAMPLE 3A
Simplify each radical expression. Assume that all variables represent nonnegative real numbers.
Solution:
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12. EXAMPLE 3B
Simplifying Radical Expressions (cont’d)
Simplify each radical expression. Assume that all variables represent nonnegative real numbers.
Solution:
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