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
Ask students what they could have done differently to still come up with the same answer– they could have simplified radical 20 to 2 radical 5 before using the distributive property.
Simplify

3. Multiplying Radical Expressions
Ask students what they could have done differently to still come up with the same answer– they could have simplified radical 20 to 2 radical 5 before using the distributive property.

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
Simplify:
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