1. Today:
 Final Exam Review
 Adding & Subtracting Radicals Review
 Rationalizing a Binomial Denominator
(Finding the conjugate)
 Class Work 4.7

2. Final Exam Review:
r = 17
4. Rewrite the equation so that y is a function of x
f(x) = 3x - 6
You take your mom out for a nice lunch to celebrate
Mother’s Day. The total comes to $28.00, so you ask your
mom if you can borrow $28.00. You plan on leaving a
15% tip. How much do you really need to borrow?

3. 20 + 45 + 3
Review: Adding & Subtracting Radicals
Review: Multiplying & Dividing Radicals
3 8 + 45

4. Class Notes Section of Notebook

5. Rationalizing a Binomial Denominator
Big picture: To remove the radical, we multiply the
binomial by another binomial, (FOIL) called its conjugate.
The conjugate is simply the same binomial with the
sign changed between terms.
The conjugate of the binomial denominator is...
-3 + 2 3 Now multiply top & bottom by the conjugate.
Simplify -3 + 2 3
-3 + 2 3

6. Multiply the Conjugates
(F.O.I.L.)
Conjugates
F. = 9
-20
9 – 20 = -13 The middle terms always cancel each other
out so you don’t really have to FOIL.
O. =
6 5 I. = -6 5 L. =

7. Conjugates
What is the conjugate? What is simplified denominator?
4
2 7
3
11 5

8. Conjugates
Practice #2:
The form of 1 we’re going
to multiply by is...
Class Work 4.7
As always, show work for credit
 5 7 6   4 5 3 5 
  7 3 7 3    3 5 7 2 5 
4
2 7
3
11 5