Anonymous

# Review,What are some examples of irrational numbers?

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Any number that can be expressed as a numerator divided by a denominator is a "rational" number. (Note rational has the root word ratio in it)

Irrational numbers usually contain a "radical" sign. like the SQUARE ROOT symbol or natuaral log function or some of the trig functions in some cases.

The best-known irrational number is the square root of 2, but any nth root of a number that is not the nth power of a whole number will do.

Then there are the famous numbers that are not just irrational, but transcendental (can't be computed using ordinary algebra) such as pi (3.14159...) and e (2.71828...).

You can tell if a number is irrational by looking at its decimal representation. If it repeats, like 3.33333... or 1.857142857142... (13/7) it's rational; if it goes on forever with no apparent pattern it's irrational (and possibly transcendental, too).

Here is one:

1.01001000100001...

This number is irrational, because its decimal representation

is aperiodic.

Another exmaple is "the number, which square is 2",

usually denoted as √2, but the proof is not as easy.

You need to prove that

1) such real number actually exists

2) it cannot be rational

Yet another example is the ratio of circumference of a

circle to its diameter, denoted as π. I heard that this

number π is proven to be irrational, and even non-algebraic,

but I don't know the proof.

• 5 years ago

Sqrt.5 + Sqrt.6 = Sqrt.11(an irrational number).

a number is irrational if and only if it's continued fraction expansion does not terminate. this means you can chose any positive whole numbers you want in your continued fraction,

as long as it never ends, and you will get only irrational numbers.

a rational number, on the other hand, has a continued fraction expansion which terminates rather " quickly".

• SS4
Lv 7

the square root of all real numbers which are not square numbers

I've never liked 6!

• Dr D
Lv 7