Simplify Radicals
Simplify Perfect Roots
• Find MULTIPLES of the Root
x4
2
x4
x
3
42  2
3
2
m9
4
93  3
m9
m
3
8
mn
2
x2 x y 4
3
63
m2
2
y
x
x
xy
2
x
m
23
m 24
m
3
x3 y 4
m
4
m 24
2
3
mn
n2
2
6
24  4  6
Perfect Squares
Perfect Cubes
82
4
16  2
4
81  3
42
3
9 3
3
27  3
16  4
3
64  4
25  5
3
125  5
36  6
49  7
Fourth Roots
Fifth Roots
5
5
32  2
243  3
Example 1
Simplify
25x 3
25x 2 x
5x x
Example 2
Simplify
3
3
54x y
8
6
6
27 2 x y y
2
3x y
2
6
3x y
2 3
23
2y
2y
2
2
2
Example 3
Simplify
3
3
4
48x y
5
3
3
86x x y y
3
2 x y 6xy
3
2 xy 6 xy
2
2
2
Example 4
Simplify
4
2x y
2 xy
48x 4 y11
23
23
6xy
6 xy
2
2
3
3
6
8 6x x y y
2
Example 5
Simplify 3 5 32x8 y 5
5 3
5
3 32x x y
5
3 2x y x
5
3
6xy x
3
5
Example 5
Simplify
3
3
48x 4 y 8
3
6
8 6x x y y
2x y
2 xy
23
23
6xy
6 xy
2
2
2