Rationalizing Radicals (and Practice)
Warm Up:
The expressions on this page might try to tempt you away from the strict mathematical rules you have learned about radical expressions.
So, work carefully to simplify each expression and think about every move you make! If an expression cannot be simplified, then say so.
Always, Sometimes, Never
• Sort your cards into the following categories
o Always True (Can you explain why?)
o Sometimes True (Give a true example and a counter-example)
o Never True (Give a counterexample)
Completed Sort:
Rationalizing Denominators
8
5
You can never have a ____________ in the denominator of a fraction!
1
2
1
12
10
3 20
Operations with Radicals Group-Pair-Solo
Group
Pair
Solo
Homework!
1.
49 x 2 y10
2.
4.
900a 4 b 6
5.
54 y 7
8.
7.
3
5
243x15
3.
8x 3 ⋅ 2 x 5
6.
75 x 3
3
− 64 y 8
27x 3
9. (3+ 9 3) − (7 − 4 3)
3x
10.
27 + 5 3 − 12
11. (5 + 3)(2 − 3)
12. (3+ 2 )(6 − 2 2 )
13.
6 ⋅ 54
14. 23 2 x 2 y ⋅ 53 6 x 4 y 4
15. 4 32 − 5 98
Rationalize the following expressions.
!
16.
!
!
18. !!
!
17.
!"
!! !
!
19. !!
!