Section 13.2
Adding, Subtracting, and
Multiplying Radical
Expressions
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Radical Expressions
Example
Combine like radicals
Solution
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Radical Expressions
Solution
Example
Continued
3. Since the radicals 4 3 x and 5 6 x have different
indexes, we cannot use the distributive law
• It’s already simplified
4
4
4. Since the radicals 3 x and 2 x  1 have different
radicands, we cannot use the distributive law
• It’s already simplified
Example
Perform the indicated operations.
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Radical Expressions
Solution
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Slide 4
Radical Expressions
Solution
Solution
Continued
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Slide 5
Radical Expressions
Adding or Subtracting Radical Expressions
Example
Perform the indicated operation.
Solution
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Radical Expressions
Adding or Subtracting Radical Expressions
Solution
Example
Continued
Perform the indicated operation.
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Multiplying Radical Expressions
Finding Products of Radical Expressions
Example
Find the product.
Solution
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Multiplying Radical Expressions
Finding Products of Radical Expressions
Solution
Example
Continued
• Verify work using a graphing calculator
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Multiplying Radical Expressions
Finding Products of Radical Expressions
Solution
Example
Continued
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Multiplying Radical Expressions
Finding Products of Radical Expressions
Solution
Example
Continued
If
n
x is defined, then
 x
n
x
In words: The nth power of the nth root of a number.
n
Example
Simplify.
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Slide 11
Multiplying Radical Expressions
Simplifying Radical Expressions
Solution
1. Multiply each term of the first factor by each term
of the second factor, and combine like radicals:
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Multiplying Radical Expressions
Simplifying Radical Expressions
Solution
Solution
Continued
Example
Simplify


2
a 3 b .
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Slide 13
Multiplying Radical Expressions
S i m p l i f y i n g t h e S q u a r e o f a R a d i c a l E x p r e s s i o n w i t h Tw o Te r m s
Solution
Another way:
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Slide 14
Multiplying Radical Expressions
S i m p l i f y i n g t h e S q u a r e o f a R a d i c a l E x p r e s s i o n w i t h Tw o Te r m s
Warning
Example
Simplify


2
a 3 b .
Solution
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Slide 15
Multiplying Radical Expressions
Example
Find the product.
Solution
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Slide 16
Multiplying Radical Expressions
Solution
Example
Continued
Find the product.
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Multiplying Radical Expressions
M u l t i p l y i n g Tw o R a d i c a l s w i t h D i f f e r e n t I n d e x e s b u t t h e S a m e R a d i c a n d
Process
To multiply two radicals that have the same index,
we use the product property:
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Slide 18
Multiplying Radical Expressions
M u l t i p l y i n g Tw o R a d i c a l s w i t h D i f f e r e n t I n d e x e s b u t t h e S a m e R a d i c a n d
Process
To multiply two radicals with different indexes but
the same radicand,
1. Write the radicals in exponential form.
2. Use exponential properties to simplify the
expression involving exponents.
3. Write the simplified expression in radical form.
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Slide 19
Multiplying Radical Expressions
Simplify Radical Expressions
Example
Perform the indicated operations. Assume that x ≥ 0.
Solution
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Slide 20
Multiplying Radical Expressions
Simplify Radical Expressions
Solution
Example
Continued
Perform the indicated operations. Assume that x ≥ 0.
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Multiplying Radical Expressions
Simplify Radical Expressions
Solution
Example
Continued
• Verify using a graphing calculator
Process
To simplify a radical expression,
1. Perform any indicated multiplications.
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Slide 22
Multiplying Radical Expressions
Simplifying a Radical Expression
Process
Process
Continued
2. Combine like radicals.
3. For any radical with index n, write the radicand as
a product of one or more perfect nth powers and
another expression that has no factors that are
perfect n-th powers. Then apply the product
property for radicals.
4. Write any radicals with as small an index as
possible.
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Slide 23