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Irrational Numbers Explained in 5 Minutes

Irrational Numbers Explained in 5 Minutes

The concept of a power allows us to write a whole new set of equations - called polynomial equations. For example..

x^2-9=0 which has a solution x=3

x^5=32 which has a solution x=2

But not all polynomial equations have easy solutions. Consider this..


It's a very simple equation to write down, but the solution is not so easy. The solution is certainly not an integer. And it's possible to prove that the solution is not a rational number, meaning it cannot be written as a fraction a/b where a and b are integers. The solution is..

x=square root of 2

The square root of 2 is an example of a new type of number. Since this new type of number is not a rational number mathematicians gave it the name "irrational number". Not exactly a creative name!

So in order to solve some polynomial equations we need yet another type of number. Now we have three types..

Integers or whole numbers {..,-3, -2, -1, 0, 1, 2, 3,..}
Rational Numbers or "fractions" a/b where a and b are integers.
Irrational Numbers which are not integers and not rational numbers.

The theme is consistent. New numbers are needed if we want to solve more equations. So, solving polynomials has so far required 3 types of numbers.

You may be wondering if 3 types of numbers are enough to solve all possible polynomials. The answer is no. But don't panic, this process does not go on forever. It turns out that just one more type of number is needed to solve all polynomials. This time mathematicians outdid themselves when it came to a name, they called this final type of number an "imaginary number". Good grief!

Content written and posted by Ken Abbott