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Radicals Homework -- Some Very Important Generalizations

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides sample problems which develop concepts related to generalizing some concepts of radicals.

Exercise 1

9 = 9 =

Exercise 2

4 = 4 =

Exercise 3

9 × 4 = 9 × 4 =

Exercise 4

9 × 4 9 × 4

Exercise 5

Based on #1-4, write an algebraic generalization.

Exercise 6

Now, give me a completely different example of that same generalization: four different statements, like #1-4, that could be used to generate that same generalization.

Exercise 7

94=94 size 12{ { { sqrt {9} } over { sqrt {4} } } } {}=

Exercise 8

9 4 9 4

  • a. What do you think is the answer?
  • b. Test by squaring back. (To square anything, multiply it by itself. So this just requires multiplying fractions!) If it doesn’t work, try something else, until you are convinced that you have a good [xxx].

Exercise 9

Based on exercises #7-8, write an algebraic generalization.

Exercise 10

9 + 4 = 9 + 4 =

Exercise 11

9 + 4 9 + 4

Exercise 12

Based on exercises #10-11, write an algebraic generalization that is not true.

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