1. Lesson #1: Simplifying Radicals (For use with Sections 7-2 & 7-3)
Please pick up the Lesson #1 example sheet found on the front table.
Complete the Warm-Up box found at the top of the front page.

2. Warm-Up: Area = 9 units2 Area = 121 units2 Area = 57.76 units23 11
7.6
x = … units
x = 5 units
x = 14 units x
Area = 45 u2 x
Area = 25 u2 x
Area = 196 u2
x2 = 45
x2 = 25
x2 =
x2 = 45
x2 = 25
x2 =

3. Answers with Radicals
The square root of a number is any number that when multiplied by itself is equal to the original number.
Example: The square root of 16 is 4 because 4  4 = 16
A square root is the inverse operation of squaring.
Example: 32 = 9 and 9 = 3
Perfect Squares – are those numbers whose square root is a whole number. 1, 4, 9,
16,
25,
36,
49,
64,
81,
100,
121,
144,
169,
196,
225,
256,
289,
324,
361,
400

4. Answers with Radicals
When answers with radicals do not have a perfect square answers, we have two options for how to leave the answer.
Approximate Answer – this is when we find the decimal equivalent of the answer round it to a specific decimal place. We use the symbol () to show that it has been rounded.
Example: = ….
12  3.46 (rounded to a hundredth)

5. Simplest Radical Form (Exact)
Simplest Radical Form (Exact) – these are answer that leave non-perfect squares inside the radical.
A radical is in simplest radical form when ALL of the following are true:
 The number under the radical symbol has no perfect squares as one of its factors.
 The number under the radical symbol is not a fraction.
 There are no radicals in the denominator.
Example: =

6. Rules for Dividing by 2 through 10
When Dividing by …
Look for a number that….. 2
Ends in 0, 2, 4, 6, 8 (the even numbers) 3
The sum of all the digits in the number is divisible by 3.
Example: 156 has = 9 and 9 is divisible by 3. So, 156 is divisible by 3. 4
If the last two digits of the number are divisible by 4.
Example: has 12 as its last two digits and 12 is divisible by 4. So, 3512 is divisible by 4. 5
Ends in 5 or 0. 6
If the number is divisible by 2 AND 3.
Example: 156/2 = 78 and 156/3= 52. So, 156 is divisible by 6. 7
Take the last digit in the number, double it, and subtract it from the remaining digits. If this result is divisible by 7, then the original number is divisible by 7.
Example: For 203, 3´2 = 6 and = /7 = 2, so 203 is divisible by 7. 8
If the last three digits of the number are divisible by 8.
Example: has 024 as its last three digits and 024/8 = 3. So, 6024 is divisible by 8. 9
Add up all the digits of the number. If the sum is divisible by 9, then the number is divisible by 9.
Example: 43,785 has = 27, and 27/9 = 3. So, 43,785 is divisible by 9. 10
If the number ends in a 0.

7. Example #1: Factor Pairs
List each of the factor pairs for the given number. Circle the perfect squares in the pairs.
(A) (B) (C) 60
1 and 18
2 and 9
3 and 6
1 and 32
2 and 16
4 and 8
1 and 60
2 and 30
3 and 20
4 and 15
5 and 12
6 and 10

8. Rule for Multiplying Radical
If two numbers are being multiplied under the same radical, then the numbers can be separated into two individual radicals.

9. Example #2: Simplest Radical Form
(A) (B)
1 and 18
2 and 9
3 and 6
1 and 32
2 and 16
4 and 8

10. Example #2: Simplest Radical Form
(C) (D)
1 and 80
2 and 40
4 and 20
5 and 16
8 and 10
1 and 150
2 and 75
3 and 50
5 and 30
6 and 25
10 and 15

11. Example #2: Simplest Radical Form
(E) (F)
1 and 80
2 and 120
4 and 60
5 and 48
6 and 40
8 and 30
10 and 24
12 and 20
15 and 16
1 and 396
2 and 198
3 and 132
4 and 99
6 and 66
9 and 44

12. Simplifying Fractions with Radical s
We can also simplify fractions that involve fractions. Let’s review a few basic rules for simplifying any fraction.
1) In this case, the 4 and 18 are divisible by 2.
2) Fractions with more than one term in the numerator can be split into two separate fractions.

13. Example #3: Fractions & Radical Form
(B)
(C)
(D)