Download Radical Review

Radical Review
I. Adding/Subtracting Radicals
Only like radicals can be added.
Add/subtract radicals like you would add/subtract like terms.
Add/subtract the “coefficients” and carry through the like radical.
Example: Add or subtract.
a. 3 7  5 7 = 8 7
b. 5 3  7 3 =  2 3
White Board Activity:
Practice: Add or subtract.
a. 4 5  7 5 = 11 5
b. 8 2  3 2 = 5 2
II. Multiplying Radicals
Multiply “outside” number x “outside” number.
Multiply “inside” number x “inside” number.
Simplify the answer.
Examples: Multiply and simplify.
a. 12  3 = 36 = 6


c. 2  3 3  2



b.
3 7  5 = 7 3  15
b.
5 2  11 = 2 5  55
62 2 3 3  6
White Board Activity:
Practice: Multiply and simplify.
a. 24  6 = 144 = 12


c. 3  5 4  3



12  3 3  4 5  6
III. Simplifying Radicals
An expression with radicals is in simplest form if no perfect square factors other than 1 are in
the “inside” number.
Steps:
1. Prime factor the number
2. Look for pairs. Write each pair as a square number.
3. Rewrite the problem using the factors from 2.
4. Take square roots as possible.
5. Multiply according to radical multiplication rules.
Outside numbers x outside numbers
Inside numbers x inside numbers
Example: Simplify the expression.
a. 48
22223
4 4 3
2·2  3 = 4 3
c. 5 96
5 2 2 2 2 23
5 4 4 6
5·2·2 6
20 6
White Board Activity:
Practice: Simplify the expression.
a. 80
2 2 2 25
4 4 5
2·2 5
4 5
c. 7 27
7 333
7 9 3
7·3 3
217 3
b.
72
2  2  2 33
4 9 2
2·3  2 = 6 2
d. -8 12
-8 2  2  3
-8 4 3
-8·2 3
-16 3
b.
84
2  2  3 7
4 21
2 21
d. -4 24
-4 2  2  2  3
-4 4 6
-4·2 6
-8 6
Some addition/subtraction problems need to be simplified before the addition/subtraction can be
completed.
Example: Add or subtract.
a. 8 5  125
8 5 5 5
13 5
b. 3 24  5 54
3 2 6  5 3 6
6 6  15 6
21 6
White Board Activity:
Practice: Add or subtract.
a. 6 3  243
6 3  33333
6 3 9 9 3
6 3  33 3
b. 5 75  2 108
5 553  2 2  2 333
5 25 3  2 4 9 3
55 3  2 23 3
6 3  9 3  15 3
25 3  12 3  13 3
IV. Dividing Radicals
Divide the “outside” number by the “outside” number if possible.
Divide the “inside” number by the “inside” number if possible.
Reduce the “outside” part of a fraction if possible.
Reduce the “inside” part of a fraction if possible.
Take a square root when possible.
Example: Simplify.
12 15
a.
3 3
b.
12  3  4
12 15
3 3
c.
2 3
6 12
2 1

6 3
15  3  5
2 3
4 5
6 12
36
36  6
16
36
16
White Board Activity:
Practice: Simplify.
25 30
a.
6 6
b.

6 6
c.
25
81

12


1
4

1
2
1 1 1
 
3 2 6
16  4
6 3

4 2
5 2
15 18
5 1

15 3
30  6  5
25 30
3
25 5
6
5 2
15 18
25  5
25
81

2
18


1
9

1
3
1 1 1
 
3 3 9
81  9
5
9
A simplified radical does not have a radical term in the denominator.
To clear radicals from a denominator, you must rationalize the denominator.
This means multiply both the numerator and denominator of the fraction by the radical term from the
denominator.
Example:
1
a. Simplify
1
3
3

3
3
.

b. Simplify
3
9
3
3

2
3 5

2
3 5
5

5
.

2 5
3 25
2 5 2 5

35
15
White Board Activity:
Practice:
2
a. Simplify
2
5

5
5
5
.

b. Simplify
2 5
25

2 5
5
5
.
2 7
5
7
2 7


2 7 7 3 49

5 7 5 7

3 7
21