Download 9.1. Simplifying Radicals - San Diego Unified School District

Date:
Topic: Simplifying Radicals
(9.1)
Warm-up: Find the square root.
1.
36 = 62
6
2.
64 = 8
2
8
3.
225 = 152
15
Simplify the radical:
4.
50= 25·2
 25  2
5 2
5.
108 = 36·3 6.
 36  3
6 3
24  4  2  3
 4 6
2 6
Rules about Radicals
If x and y are non-negative
numbers, then:
x y
xy
If a and b are non-negative
numbers, and b ≠ 0, then:
a
b

a
b
Example:
2· 3 = 2·3 = 6
Example:
2
10


15
3
15
10
Simplifying Radicals
There are two ways to simplify radicals:
1. Dividing down
2. Finding perfect squares
Dividing Down
Finding Perfect Squares
40
22  25
4 10
2 10
2 40
2 20
2 10
5
32  16  2
4 2
Multiplying Radicals
Multiply the numbers
outside of the radicals
Multiply the numbers inside
the radicals
a b c d 
ac bd
Example:
5 3 7 2   5·7

3 2 
35 6
Example: Multiply the radicals
5 2 6 6 
 5  6 2·6
 30 12
 30  4  3
 30  2 3
60 3
Example: Square the radicals
3 5 
2
  
 3 5 3 5 OR
3
 9 25
 95
 95
45
2
45
5
2
Fractions with Radicals
When a radical is in the
denominator, we must rationalize
the denominator of the fraction.
To do this, we multiply the fractions’
numerator and denominator by the
radical in the denominator.
a
b
·
2
·
2
2

5 2
5 2
2 =
2
2
 
b
a b
b
Example:
5
b

a b
 b
2
Example: Simplify the rational and be sure to rationalize the
denominator.
5 2
6
·
6
6

5 12
 
6
2

5 12
6
5 4 3

6
5  2 3 10 3 ¸2  5 3


3
6 ¸2
6