1. Don’t be squared – get started!
1/18/2017: We will learn to use perfect square factors to simplify radicals.
Do Now!
Have Out:
- Today’s hand-outs
- HW from last class
Do Now:
Don’t be squared – get started!
Agenda!
Guided Notes!
GP!
IP!
ET!
Homework!
Handout
(11 problems)

2. We will learn to use perfect square factors to simplify radicals.
Hook: How are these equivalent?
45 = 3 5

3. Introduction
Numbers like 1, 4, 9, 16, 25, 36, etc. are called _______________ because they are the product of an integer times itself.
perfect squares
EX: 4 × 4 or 42 = 16
When you take the square root of a perfect square, the result is a _____________.
whole number

4. Not a perfect square? 8 and 9 (Because 82 = 64 and 92 = 81) ≈ 8.66
What 2 integers is between? (Mental Math)
8 and 9 (Because 82 = 64 and 92 = 81)
2. What is the approximate value of ? (Calculator)
≈ 8.66
3. We can also simplify the radical…

5. Background Vocabulary
radical
radicand
This is also called a “Square Root”

6. Steps to Simplify Radicals
Find the largest __________________ of the radicand, excluding 1.
perfect square factor
Note: A factor is a number that divides evenly into a given number with no remainder.
Write the number as the _______ of the perfect square factor and its other factor.
product
Split each factor into two separate _______.
radicals
Simplify the _____________ radical.
perfect square

7. Example 1: Check for perfect square factors of 75:
Find the largest perfect square factor of 75, excluding 1.
Check for perfect square factors of 75:
4, 16, 25, 36, 49, 64
Write the radicand as the product of the perfect square factor and its corresponding factor.

8. Example 1: Split each factor into two separate radicals.
Simplify the perfect square radical.

9. Example 2: 3 First Step: Multiply the radicals72
Then…try to simplify on your own
Lastly, check if you have the same answer as your neighbors.

10. Discussion Questions
What happens if you do not use the largest perfect square factor when simplifying?
The radicand will still have perfect square factors and can be further simplified by repeating the process.
What if the radicand does not have any perfect square factors other than 1?
The radical is already in simplest form.

11. More Simplification…
What if the number under the radical is a fraction?

12. Example 3: Rationalizing the Denominator
1. Separate the numerator and denominator into separate radicals.
Is this radical in simplest form?
2. Simplify each radical if possible.
We must rationalize the denominator.
No, we cannot have a radical in the denominator.

13. Example 3: Rationalizing the Denominator
3. Multiply both the numerator and denominator by the root.
Why can we do this without changing the result?
4. Simplify.

14. Example 4: Rationalizing the Denominator
Simplify the radical.
Rationalize the denominator.