Multiplying Binomial Radial Expressions and Rationalizing with Conjugates.

1
Multiplying Binomial Radial Expressions and
Rationalizing with Conjugates.

• MA.912.A.6.2 Add, subtract, multiply, and divide
  radical expressions (Square roots and higher)

2
Multiplying Radical Expressions
Distributive Property
Product Property Of Radicals
Simplify
3
Multiplying Radical Expressions
4
Multiplying Radical Expressions
Since there are no like terms, you can not
combine.
5
Conjugate Binomials
The conjugate of

When you multiply conjugate binomials, The
product will be The Difference of
Squares.
6
Conjugate Binomials
The conjugate of

7
Multiplying Conjugates
What other method would yield the same answer
with less work?
8
Multiplying Conjugates
9
Rationalizing Using Conjugates
You should recall that a radical expression
is not considered simplified if there is a
radical in the denominator. The process of
eliminating the radical in the denominator is
called rationalizing.
10
Rationalizing Using Conjugates
When the denominator contains a binomial with
a radical, one must multiply by the conjugate in
order to rationalize the denominator.
Multiplying by 1 does not change the value of the
number.
NO RADICAL!
11
Rationalizing Using Conjugates
Multiply by the conjugate.
Multiply numerators Multiply denominators.
Combine like terms
Finished on next slide.
12
Combine like terms
Never leave Negative in the Denominator!
Distribute