image map Research Projects for Intermediate Algebra

Chapter 5 Projects
RATIONAL EXPONENTS AND ROOTS

RESEARCH PROJECT: Connections

Although it may not look like it, the three items shown below are related very closely to one another. Your job is to find the connection.

Begin your research by reworking Problem 43 in Problem Set 4.5. (This is for those students using Intermediate Algebra: Concepts and Graphs, 3/e, by Charles P. McKeague.) Then find a decimal approximation to each of the fractions you found in Problem 43. Use inductive reasoning to find a decimal approximation to the continued fraction that is accurate to the nearest thousandth. Once you have this decimal approximation, compare it with what you know about the golden ratio, which is the ratio of the length to the width in the golden rectangle.

Once you see how the three items are related, write your results in essay form so that anyone who has successfully completed intermediate algebra could use it as a guide to discovering the relationship that you have discovered.

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