Name: ________________________________________ Date: __________________ Period: ______________
6.4B Simplifying Square Roots
To simplify square roots that are not perfect squares, use the following property:
Find the largest factors of the radicand that
are also perfect squares. Then take the square
root of the perfect square factor(s) and put the
result(s) on the outside of the radical sign.
Example 1: Simplify √50
Example 2: Simplify √24
Example 3: Simplify √45
You Try 1: Simplify √98
You Try 2: Simplify √20
You Try 3: Simplify √(15)(60)
You Try 4: Simplify √75
You Try 5: Simplify √(13)(52)
You Try 6: Simplify √(16)(12)(27)
Apply the radical sign to the numerator
and denominator. Then simplify as much
as possible using perfect squares and the
product property of square roots.
Example 1: Simplify √
11
16
Example 2: Simplify √
13
144
Example 3: Simplify √
27
100
You Try 1: Simplify √
23
You Try 2: Simplify √
64
65
You Try 3: Simplify √
121
48
4
Homework: Simplify the following radical expressions.
1. √192
2. √40
3. √325
4. √98
5. √125
6. √18
7. √300
8. √(12)(36)
9. √63
10. √𝑎2
11. √
16.
17
36
√
13
52
12. √
13
100
17. √
76
169
13. √
18. √
33
144
5
𝑏2
14. √
35
15. √
729
19. √
98
121
11
25
20. √
40
36