Download Simplifying Radical Expressions

11.3 Simplifying Radicals
Simplifying Radical Expressions
A radical has been simplified when its
radicand contains no perfect square factors.
Product Property for Radicals
ab  a  b
Steps
1. Factor the radicand into a perfect square if
possible
2. If there is an exponent make it even by
using rules of exponents (to take sq rt of
exponent divide by 2)
3. Simplify by taking the square root of
perfect squares and leaving non perfect
squares under the radical
Assume all variables are
nonnegative
• This means take the principal root and no
need for absolute value
Simplify:
45
9 5
3 5
Simplify:
49 x
49  x
7 x
Simplify:
52t
4  13t
2 13t
Simplify:
12
x
x 
2
6
x
6
Square root of a variable to an
even power = the variable to
one-half the power.
Simplify:
y
y
88
44
Square root of a variable to an
even power = the variable to
one-half the power.
Simplify:
x  x x
12 1
13
x  x
12
x
6
x
x
Simplify:
27
x  x
26
13
x
x
Simplify:
36x
8
6  x
2
6x
4
8
Simplify:
10
49 y
7y
5
45x
Simplify:
6
9x  5
6
3x
3
5
Simplify:
50 y
7
25 y  2 y
6
5y
3
2y
Simplify:
48y
9
16 y  3 y
4
4y
2
3y
Simplify:
80 y
16
16 y  5
16
4y
8
5
 y  3
36
Simplify:
 y  3
18
Simplify:
2 x  20 x  50
2
2x  10 x  25
2
2
x  5
2 x  5
2
y  6y  9
2
Simplify:
 y  3
y 3
2
4  x  5
10
Simplify:
4
 x  5
2  x  5
10
5
50  y  7 
9
Simplify:
25  y  7   2  y  7 
8
5 y  7
4
2  y  7
Simplify:
36x
3
6x x
2
8
x
y
448x
y
Simplify:
4
7
3
7y
4x y  112 y
4
6
2x y  4  28y
2
3
2 x y  2  4  7y
2
3
Try these
3 200
5r
2
4 3
32r s
Cube Roots
3
8
3
27
3
81
3
125
Assignment:
Page 493
(2-44 even, 46-55all)
Page 494 (1-16) all