An **Irrational Number** is a actual number that **cannot** be written as a basic fraction.

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Irrational way **not Rational**

Let"s look in ~ what renders a number rational or irrational ...

### Rational Numbers

A **Rational** Number **can** be written as a **Ratio** of 2 integers (ie a an easy fraction).

### Irrational Numbers

But part numbers **cannot** be written as a proportion of 2 integers ...

...they are called **Irrational Numbers**.

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

We **cannot** write down a simple fraction that equals Pi.

The well-known approximation the 22/7 = 3.1428571428571... Is close but **not accurate**.

Another clue is that the decimal goes on forever without repeating.

## Cannot Be written as a Fraction

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

So we can tell if it is reasonable or Irrational by do the efforts to compose the number as a basic fraction.

**Example: 9.5** have the right to be written as a simple fraction like this:

9.5 = *19***2**

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

Here are some much more examples:

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

1.75 | 74 | Rational | ||

.001 | 11000 | Rational | ||

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

## Square root of 2

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

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

**The prize is the square root of 2**, which is** 1.4142135623730950...(etc)**

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

... In fact we **cannot** compose the square root of 2 using a proportion of 2 numbers ...

... (you have the right to learn **why** top top the Is that Irrational? page) ...

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

## Famous Irrational Numbers

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The number | ||

The gold Ratio is an irrational number. The first few digits look choose this: | ||

Many square roots, cube roots, etc are likewise irrational numbers. Examples: But √4 = 2 is rational, and also √9 = 3 is reasonable ... ... For this reason ## Note on multiplying Irrational NumbersHave a look in ~ this: π × π = π2 is known to beirrational but √2 × √2 = 2 is rational So be cautious ... Multiplying irrational numbers ## Fun truth .... Apparently But pendant of 434,435,1064,2022,3987,1065,3988,2023,2990,2991 Surds Square Roots scientific Calculator Is it Irrational? numbers Index |