Chapter 2: Square Root and Real Numbers

Getting the Square Root

If the square of a number n is n² or n * n, then the square root of a number is $\frac{\mathrm{ n(n)}\mathrm{}}{\mathrm{ n}}$.
Example: (for the whole website, we will be depicting square root as the sqrt(n) function)
sqrt(4) = 2

Rational Numbers

These are numbers that can be expressed with a fraction $\frac{\mathrm{ p}\mathrm{}}{\mathrm{ q}}$ of two integers, a numerator p, and a non-zero denominator q. For example, 6 is a rational number because 6 can represent a fraction $\frac{\mathrm{ 6}\mathrm{}}{\mathrm{ 1}}$.

Integers

These are numbers that is not a decimal. Examples of these are: 3, -17, 890, and 2453.

Whole Numbers

These are all numbers that in an integer excluding the negatives. Examples of these are: 5, 0, 16, 239.

Natural Numbers

Basically all whole numbers excluding zero. These are also known as counting numbers. Example: 1, 2, 3...

Irrational Numbers

They are the opposite of rational numbers, as you may have guessed. They cannot be expressed with a fraction.
Examples:

• pi = 3.14159265358979...
• e = 2.71828182845904...
• sqrt(2): 1.414213562373095...

Before we head to calculating equations with rational and irrational numbers, we must know what a term is. A term is used for forming equations.
The examples of a term are:

• 5
• 5(sqrt(6))
• 2π

Calcuating Equations with Rational and Irrational Numbers

You may think this will be hard. It is, if you really try to find the exact values of a number. So we will just leave the irrational numbers as is. For example:
$$\frac{\mathrm{52}+\mathrm{6(sqrt(2))}}{2}\mathrm{ +}3(sqrt(2))$$
Step 1: Divide.

$$\mathrm{26\; +\; 3(sqrt(2))}+\mathrm{3(sqrt(2))}$$
Step 2: Add the like terms.

$$\mathrm{26}+\mathrm{6(sqrt(2))}$$

You're done! Let's try another example: $$\frac{\mathrm{39}+\mathrm{12(sqrt(3))}}{3}\mathrm{ +}7(sqrt(5))\mathrm{-\; sqrt(3)}$$
Step 1: Divide. $$\mathrm{13}+\mathrm{4(sqrt(3))}\mathrm{ +}7(sqrt(5))\mathrm{-\; sqrt(3)}$$
You're done! Remember: you can't combine unlike terms.