Unit 7
Notes: Simplifying a Square Root Using the Product Rule
Perfect Squares:
Perfect Square Roots:
12
=
72
=
1
=
49 =
22
=
82
=
4
=
64 =
32
=
92
=
9
=
81 =
42
=
102
=
16 =
100 =
52
=
112
=
25 =
121 =
62
=
122
=
36 =
144 =
 Define a Rational Radical: ____________________________________
 Define an Irrational Radical: ____________________________________
 State the Product Property for Radicals:
____________________________________
Helpful Tips to Simplify Irrational Radicals:
1. Factor inside number into prime factors or perfect squares.
2. Take out pairs of prime factors or roots of perfect squares.
3. Multiply numbers in front of radical with anything that hops out.
EX)
12
EX)
2 8
EX)
56
 State the Relationship Between Squares and Square Roots
_______________________________________________________________
EX)
132
EX)
 8 2
 2
EX) 2 5
*More Practice (Attempt to use mental math!)
Evaluate or simplify the following. If the root is irrational, state the simplified
answer in radical form.
1.
64
2.
32
 2
3. 3 7