Simplifying Radical Expressions

1
Section 7.3

• Simplifying Radical Expressions

2
Product Property

• If the nth roots of a and b are real, and
• ngt2 is an integer, then
• Note requires that the indices (n) be the same.

3
Examples
4
Simplifying using the Product Property

• A radical expression is simplified if the
  radicand does not contain any factors that are
  perfect powers of the index.
• How to
• Write each factor of the radical as the product
  of 2 factors, one a perfect power of the index.
• Write the radicand as the product of 2 radicals,
  one of which contains perfect squares.
• Take the nth root of each perfect power.

5
Examples
6
Example
7
More examples, combining multiplying and
simplifying
8
Quotient Property to Simplify

• If nth roots are real, b not 0, and ngt2 is
  integer, then

9
Examples
10
What if the roots arent the same index?

• Deal with this problem using rational exponents.
• Cannot use the Product Property

11
Example