Algebra
Sec 11-2
Simplifying Radical Expressions
32  9
9 3
( 3) 2  9
9  3
Every positive number has two square roots.
We will us the following rules when working with square roots.
Positive square root
16 
Negative square root  25 
Both square roots
 100 
Ex 1)
Ex 2)
36
 49
Ex 3)  121
Ex 4)
49
Simple Radical Form
We sometimes leave the
in our answer when the “radicand” (number under the
radical) is NOT a perfect square. No decimal answers!
Rules for Simple Radical Form
1. The radicand has no perfect square factors other than 1.
2. The radicand is not a fraction.
3. There are no radicals in the denominator.
Product Property of Radicals
xy  x  y
Ex 1)
50
Ex 2)
Ex 4)
200n3
Ex 5)
72
Ex 7)
48
Ex 8)
120
99
Ex 3)
27x 2
Ex 6)
24
Ex 9)
60xy 3 z 2
We can also use the property in reverse:
Ex 10)
6 6
Ex 13) 2 6  3 3
Ex 11)
Ex 14)
8  10
( 12) 2
Ex 12)
5x  12 xy
Quotient Property of Radicals
x

y
Ex 1)
3
16
Ex 2)
x
y
16
25x 2
Ex 3)
5n
400
Sometimes, it is easier to simplify under the radical first.
Ex 4)
18
9
Ex 5)
Ex 7)
100n
4n
Ex 8)
27
9
Ex 6)
5
20
x3 y
x
Sometimes it is not!
Ex 9)
5
25
Ex 10)
2y
36 y 2
Ex 11)
)
16 x 2
7
36