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

For more information, see cubes and cube roots.

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.