Objective - To simplify irrational roots.
a  b  ab
Example:
4  9  36
2  3  6
ab  a  b
20 
4 5 
4 5
2 5 2 5
20  2 5 Check using a calculator!
Simplify.
18 
9 2 
9 2
3 2 3 2
18 
63
To simplify the number must have a perfect square factor.
35 
35
35
1 35
5 7
No perfect
square factors
Can’t be
simplified
List the perfect square factors from 1 to 300.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,
169, 196, 225, 256, 289
Simplify each irrational root.
1) 50  25 2
4) 12  4  3
 25  2
5 2
2) 27  9 3
 4 3
2 3
5)
45  9 5
 9 5
3 5
6)
28  4  7
 4 7
2 7
 9 3
3 3
3) 98  49  2
 49  2
7 2
Simplify.
72
72
72
36 2
9 8
36  2
9 8
Perfect square
6 2
3 8
3 4 2
8  42
3 4 2
3 2  2  6 2
Simplify each irrational root.
1) 32  16 2
4)
 16  2
4 2
2) 200  100 2
 100  2
 10 2
3) 80  16 5
 16  5
4 5
30  30
Already
Simplified
5)
48  16 3
 16  3
4 3
6) 5 60  5 4  15
 5 2  15
 10 15
Simplify each irrational root.
7) 5 54  5 9 6
10) 3 40  3 4  10
 5 3 6
 15 6
 3 2 10
 6 10
8) 7 48  7 16  3 11) 180  36  5
 7  4  3
 28 3
9) 5 42  5 42
Already
Simplified
 36  5
6 5
12) 4 9
Not a Real Number