0.2 Simplifying Square Roots
Warm Ups
Find the square root of each number.
1.) 169
2.) 324
3.) 484
4.) 625
5.) 225
Product Property of Square Roots
ab
=
a
b
where a and b
25 7 =
0.
7
25
7
= 5
3 64
Simplifying a Radical Expression
Simplest Form
No factor under the radical sign has any
perfect square factor other than 1.
There are no fractions under the racical
sign.
Factor using greatest perfect square
factors.
Use the product property of Square Roots
675 =
=
No radical sign in the denominator of
any fraction.
25 9 3
9
25
3
=5 3
= 15
3
3
Simplifying Variable Expressions
Try it!
48 x
2
=
Factor using GREATEST perfect
square factor!
3 16 x
2
=
3
=
3
= 4x
147x
16
4
3
x
x2
7
3x
Quotient Property of Square Roots
a
=
b
49
=
100
13
81
=
a
a
0
72f2
=
9
36 2 f2
9
b
=
6f 2
= 2f 2
3
b >0
49
100
13
9
7
= 10
Try It...
15
49x2
15
7x