1. Chapter 8
Section 3

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. 2 3

3. Add and subtract radicals.
Objective 1
Add and subtract radicals.
Slide 8.3-3

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.
Slide 8.3-4

5. Adding and Subtracting Like Radicals
EXAMPLE 1
Adding and Subtracting Like Radicals
Add or subtract, as indicated.
Solution:
It cannot be added by the distributive property.
Slide 8.3-5

6. Simplify radical sums and differences.
Objective 2
Simplify radical sums and differences.
Slide 8.3-6

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.
Slide 8.3-7

8. Simplifying Radicals to Add or Subtract
EXAMPLE 2
Simplifying Radicals to Add or Subtract
Add or subtract, as indicated.
Solution:
Slide 8.3-8

9. Simplify more complicated radical expressions.
Objective 3
Simplify more complicated radical expressions.
Slide 8.3-9

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 3
Simplifying Radical Expressions
Simplify each radical expression. Assume that all variables represent nonnegative real numbers.
Solution:
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12. Simplifying Radical Expressions (cont’d)
EXAMPLE 3
Simplifying Radical Expressions (cont’d)
Simplify each radical expression. Assume that all variables represent nonnegative real numbers.
Solution:
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