Transcript Do Now:

Do Now:
a. 81  81  9
16
4
16
b. 5




7



5
7
c.
 7 * ?  7
d.
(2  6)(8  6)


? 7
 22  10 6
 5 *  ____?____   9
e. 4
?  4 5
1
2
If we tried to write as a decimal,
we would not be able to.
?

1.414213562 ...1
• We cannot divide by a non-terminating

decimal number. We must rationalize
the denominator.
We must RATIONALIZE THE
DENOMINATOR!!!
• Definition: To rationalize the
denominator means to rewrite the
fraction so the denominator is a rational
number.
We must use a number’s conjugate for this.
Conjugate:
• Definition: (Don’t write this down)
Numbers are conjugates of one another
if they solve the same irreducible
polynomial equation.
Examples of conjugate pairs:
(1 6) and (1 6) ( 2  3) and ( 2  3)
( 5) and ( 5)
(11 5 3) and (11 5 3)
Find the conjugates of the
following irrational numbers:
8 Conjugate: - 8
 2

Conjugate:
2
4  2 Conjugate: 4 + 2
1 7 Conjugate: 1- 7

13  7 Conjugate:

13  7
Rationalize the Denominator:
1  2   2  2
2




2
2
2  2   4
Tip: If the denominator is a simple radical (like it is
here), you can just multiply by itself to avoid
dealing with the negative sign.