Changing the denominator of a fraction that contains a radical. Finding the conjugate of a binomial and using the conjugate to rationalize the denominator.

1. Lesson 2 4th
March 07, 2014
Lesson 2 - Division and Radicals
I. Review
A. 35
C. 5 7
B. 35
D. 7 5
A. 6 5
C. 25 6
B. 6 25
D. 5 6
A. 49
C. 7
B. 7 7
D. 7
A. 64
C. 8 8
B. 8
D. 8
II. Rationalizing Denominators
Just like when we solve 5x = 11 and we get
where we must solve:
for x, it will happen
we will get
This answer is correct, but it is considered bad etiquette to leave a
radical in the denominator. So how can we change a number's "look"
without changing its value?
Multiply by the number 1!
But we will use a "magic" number 1 to do this!

2. Lesson 2 4th
March 07, 2014
Examples:
2.
1.
3.
4.
6.
5.

3. Lesson 2 4th
March 07, 2014
7.
9.
8.

4. Lesson 2 4th
March 07, 2014
III. Conjugates
Def: A conjugate is when you change the middle sign of a binomial
Ex. The conjugate of a + b is a - b
State the conjugates of:
a. h + k
b.
c.
d.
What happens if we multply something by its conjugate?
or not?
Pick two, what happens if you multiply a binomial times itself?
Times its conjugate?
a. h + k
b.
c.
d.

5. Lesson 2 4th
March 07, 2014
Examples:
1.
2.
IV. Quadratic Formula Review
At times, we would get answers when doing the quadratic formula, as
below, let's practice simplifying them to proper forms:
Think - 1. Simplify Radical
1.
2. Find a GCF
2.
3. Reduce

6. Lesson 2 4th
March 07, 2014
3. Solve using the quadratic formula