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Questions and Answers
What is the proof that √3 is irrational?
What type of number is √3?
How can √3 be expressed in terms of rational numbers?
What can be concluded about the nature of √3?
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What is a Lewis dot structure?
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How does a Lewis dot structure represent bonding?
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What do lone pairs of electrons represent in a Lewis dot structure?
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How does a Lewis dot structure help in understanding the properties of a molecule?
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What is the purpose of a Lewis dot structure?
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What does a lone pair of electrons represent in a Lewis dot structure?
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How does a Lewis dot structure represent bonding?
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What does a Lewis dot structure help in understanding?
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Study Notes
Proof of Irrationality of √3
- The proof that √3 is irrational involves assuming the opposite, i.e., √3 is rational, and then arriving at a contradiction.
- This is done by showing that the assumption leads to a fraction with an even numerator and denominator, which contradicts the initial assumption.
Classification of √3
- √3 is an irrational number, which means it cannot be expressed as a finite decimal or a ratio of integers.
Expression of √3 in Terms of Rational Numbers
- √3 can be expressed as a non-repeating, non-terminating decimal, but it cannot be expressed as a finite fraction of rational numbers.
Nature of √3
- The nature of √3 is that it is an irrational number, which is a fundamental concept in mathematics.
Lewis Dot Structure
- A Lewis dot structure is a graphical representation of a molecule's bonding and valence electrons.
Representation of Bonding in Lewis Dot Structure
- In a Lewis dot structure, bonding is represented by drawing lines between atoms to indicate the sharing of electrons.
Representation of Lone Pairs in Lewis Dot Structure
- Lone pairs of electrons in a Lewis dot structure represent pairs of electrons that are not involved in bonding.
Significance of Lewis Dot Structure
- A Lewis dot structure helps in understanding the properties of a molecule, such as its shape, polarity, and reactivity.
- The purpose of a Lewis dot structure is to provide a visual representation of a molecule's electronic structure and bonding.
Importance of Lewis Dot Structure
- A Lewis dot structure helps in understanding the nature of chemical bonding and the behavior of molecules.
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