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ehj
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How do you show that the cubic root of two + the square root of two is irrational? I can easily show that each of these numbers is irrational, but not the sum :/.
Proove that the cubic root of 2 + the square root of 2 is irrational
- Thread starter ehj
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- Cubic Irrational Root Square Square root
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Homework Help Overview
The discussion revolves around proving the irrationality of the sum of the cubic root of 2 and the square root of 2. Participants explore the nature of irrational numbers and their sums, particularly focusing on the characteristics of the individual components.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Some participants attempt to reason through the properties of irrational numbers and their sums, questioning whether the presence of infinitely many decimal places in both components guarantees the irrationality of their sum. Others challenge this reasoning by providing counterexamples of rational sums.
Discussion Status
The discussion includes various viewpoints on the nature of irrational numbers and their sums. While some participants express confusion about the validity of certain arguments, others propose a potential proof, indicating a mix of exploration and clarification without reaching a consensus.
Contextual Notes
Participants are navigating the complexities of irrational numbers and their sums, with some expressing uncertainty about the implications of decimal representations. The original poster's attempt to establish a proof suggests a deeper inquiry into the properties of these mathematical constructs.