## 12 Questions

What is the proof that √3 is irrational?

It cannot be expressed as a fraction of two integers

What type of number is √3?

Irrational number

How can √3 be expressed in terms of rational numbers?

It cannot be expressed in terms of rational numbers

What can be concluded about the nature of √3?

It is not a rational number

What is a Lewis dot structure?

A Lewis dot structure is a diagram that shows the bonding between atoms in a molecule and the lone pairs of electrons that may exist in the molecule.

How does a Lewis dot structure represent bonding?

A Lewis dot structure represents bonding by using dots or crosses to represent the valence electrons of the atoms involved in the molecule.

What do lone pairs of electrons represent in a Lewis dot structure?

Lone pairs of electrons in a Lewis dot structure represent non-bonding pairs of electrons that belong to a single atom.

How does a Lewis dot structure help in understanding the properties of a molecule?

A Lewis dot structure helps in understanding the properties of a molecule by showing the arrangement of atoms and the distribution of valence electrons.

What is the purpose of a Lewis dot structure?

To represent the bonding and arrangement of valence electrons in a molecule.

What does a lone pair of electrons represent in a Lewis dot structure?

A pair of non-bonding electrons that are not shared with another atom.

How does a Lewis dot structure represent bonding?

By using dots or lines to show the sharing or transfer of valence electrons between atoms.

What does a Lewis dot structure help in understanding?

The properties of a molecule based on its electron arrangement and bonding.

## 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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