4
=2
16
=4
25
=5
100
= 10
144
= 12
9.3 - Simplifying Square Roots
(Radicals)
Standard 2.0
Simplifying Square Roots
1) Find factors of the number that are a perfect square (Twins)
2) Find the square root of the perfect square and put it in front
3) Leave the leftover factor inside the square root sign
Examples
18
 9  2  3 3 2
12
 43  2 23  2 3
3 2
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
8
=
4*2 =
2 2
20
=
4*5
=
2 5
32
=
16 * 2 =
4 2
75
=
25 * 3 =
5 3
40
=
4 *10 = 2 10
48
=
16 * 3 =
4 3
80
=
16 * 5 =
4 5
50
=
25 * 2 =
5 2
75
=
25 * 3 =
5 3
80
=
16 * 5 =
4 5
Fractions Involving Square Roots
• You can cancel out common factors first
56

7
7 8

7
8  42 2 2
Examples
4

9
32

50
2*2

3*3
16 * 2

25 * 2
2
3
16 4

25 5
3
6
You can never
have a square in
the denominator
(bottom) of a
fraction.
There is an agreement
in mathematics
that we don’t leave a radical
in the denominator
of a fraction.
1
3
The same way we change the
denominator of any fraction!
1 1 3 3


4 4  3 12
We multiply the denominator
and the numerator
by the same number.
1 1 3 3


4 4  3 12
By what number
can we multiply the bottom by?
to change it
to a rational number?
1
3
3  3 
1
3
2
3  3
1
1 3
3


3
3 3
3
Rationalize the denominator:
2
4 2 4 2
4
2 2


2
2 2
2
Rationalize the denominator:
8

12
96
8 12


12 12 12
6
4 6

12
3
3
5

10
3

12
1
7
Homework
• Page 514 # 38 – 44
&
• Page 515 # 47 – 52