10.2
Simplifying Radical Expressions
A radical expression is in simplest form if and only if:
1. The radicand has no perfect square factors other than one.
2. There are no fractions in the radicand
3. The denominator does not contain a radical expression.
Simplify the following:
50
Consider
x2
When finding the principal square root of an expression
containing variables, be sure that the result is not
negative.
x2
?
= x
(What if x = -3 ? )
?
(-3)2 = -3
9
3
?
= -3
= -3
When the exponent of the variable inside a radical is even
and the simplified exponent is odd, must use absolute
value.
x2 = | x |
2
x5 = x
x3 = x x
x 6 = x3
x
Simplify:
4
5
32 x y z6
x 4 = x2
7
9
48
8
32
50
7
6
35
15
24
x3
Multiply:
(
3
+
5
(( 3
-
5
(
Simplify:
4
-
3
2
2
4
+
5