An **Irrational Number** is a real number the **cannot** be written as a an easy fraction.

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Irrational way **not Rational**

Let"s look in ~ what makes a number reasonable or irrational ...

### Rational Numbers

A **Rational** Number **can** be created as a **Ratio** of 2 integers (ie a simple fraction).

### Irrational Numbers

But part numbers **cannot** be created as a proportion of two integers ...

...they are dubbed **Irrational Numbers**.

### Example: **π** **(Pi)** is a well known irrational number.

We **cannot** compose down a simple portion that equates to Pi.

The famous approximation that 22/7 = 3.1428571428571... Is close yet **not accurate**.

Another clue is the the decimal goes on forever there is no repeating.

## Cannot Be written as a Fraction

It is **irrational** because it can not be written as a **ratio** (or fraction),**not since it is crazy!**

So we have the right to tell if the is rational or Irrational by do the efforts to create the number together a basic fraction.

**Example: 9.5** deserve to be written as a simple fraction like this:

9.5 = *19***2**

So it is a **rational number** (and for this reason is **not irrational**)

Here space some much more examples:

Number as a portion reasonable or**Irrational?**

1.75 | 74 | Rational | ||

.001 | 11000 | Rational | ||

√2(square source of 2) | ? | Irrational ! |

## Square source of 2

Let"s look in ~ the square root of 2 more closely.

When we draw a square of size "1",what is the distance across the diagonal? |

**The price is the square source of 2**, i m sorry is** 1.4142135623730950...(etc)**

But that is no a number prefer 3, or five-thirds, or anything choose that ...

... In truth we **cannot** compose the square root of 2 utilizing a ratio of 2 numbers ...

... (you can learn **why** on the Is it Irrational? page) ...

... And so we know it is **an irrational number**.

## Famous Irrational Numbers

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The number | ||

The golden Ratio is one irrational number. The first few digits look choose this: | ||

Many square roots, cube roots, etc are additionally irrational numbers. Examples: But √4 = 2 is rational, and √9 = 3 is rational ... ... So ## Note on multiply Irrational NumbersHave a look at this: π × π = π2 is well-known to it is inirrational yet √2 × √2 = 2 is rational So be mindful ... Multiplying irrational numbers ## Fun facts .... Apparently But pendant of 434,435,1064,2022,3987,1065,3988,2023,2990,2991 Surds Square Roots clinical Calculator Is it Irrational? numbers Index |