# List of Notes - Category: Irrational Numbers

## Squares and Square Roots

To square a number, multiply it by itself.

For, example, square of 5 is 5\times5=25.

## Perfect Cube

Perfect cube is a result of cubing whole number by itself.

Whole number 0 1 2 3 4 5 6 7 8 9 10 Perfect cube (cube of a whole number) 0 1 8 27 64 125 216 343 512 729 1000

## Nth Root

Similarly to square root and cube root, we can define nth root.

Nth root of a number b is such number a, that a^n=b.

Notation for nth root is following: huge color(purple)(root(n)(b)).

Square root is 2nd root, which is sqrt(b) (we just don't write 2).

## What is Irrational Number

Irrational number is a number, that is not rational.

What does that mean?

It means, that we can't represent irrational number as a fraction, decimal with finite number of digits, or repeating decimal.

## Irrational Numbers on a Number Line

Since each irrational number can be represented as infinite decimal, then we can proceed in the same way, as we did when placed decimals on a number line.

pi~~3.14, so it is slightly to the right of 3.

## Real Numbers

Real numbers are rational numbers plus irrational numbers.

Since rational numbers include integers and fractions, then real numbers include:

• integers {..., -5,-4,-3,-2,-1,0,1,2,3,4,5,...}
• fractions (proper, improper, mixed numbers)
• irrational numbers (like sqrt(2), root(3)(-15), pi, e etc.)

Set of real numbers, i.e. group of real numbers, is denoted by RR.