3. 5
2+√3
● √3
● √3
5
2+√3
= =
( )
● √3
3
5
2√3 +
This is a problem as we still have a radical in the
denominator. To clear a binomial, we must multiply by the
of the existing binomial. (See 11-1 for definition)
The conjugate in this case is: 2 - 3. The two binomials form
a difference of squares. The middle terms cancel each other.
The result is the between the first term squared
and the third term squared. Try it. = 10 - 5√3
Rationalizing the Denominator
9. Simplify. All variables represent nonnegative numbers.
Quotient Property of
Square Roots.
Simplify.
Simplify.
Quotient Property of
Square Roots.
Simplify.
A. B.
Operations w/Radical Expressions
10. Simplify. All variables represent nonnegative numbers.
Simplify.
Simplify.
Quotient Property of
Square Roots.
Quotient Property of
Square Roots.
Simplify.
A. B.
Operations w/Radical Expressions
11. Simplify. All variables represent nonnegative numbers.
Quotient Property of
Square Roots.
Factor the radicand using
perfect squares.
Simplify.
Operations w/Radical Expressions
12. Example 4A: Using the Product and Quotient Properties Together
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Write 108 as 36(3). Product Property.
Simplify.
Operations w/Radical Expressions
13. Using the Product and Quotient Properties Together
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Simplify.
Operations w/Radical Expressions
14. Simplify. All variables represent nonnegative numbers.
Quotient Property.
Write 20 as 4(5).Product Property.
Simplify.
Operations w/Radical Expressions
15. Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product
Property.
Simplify.
Write as .
Operations w/Radical Expressions
