irrational numbers of 3 and 4?


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David Shabazi answered

Irrational numbers have a long chain of numbers occurring after the decimal point, like pi for instance.

Pi = 3.1415926535897932384626433832795...(continued)

3 isn't an irrational number itself, because there isn't a never-ending chain of numbers that goes along with it. It's quite literally just 3.0, and is also notably a prime number. So its factors are 1 and 3, and those are the two numbers you can use to multiply together to get 3 without getting a decimal answer.

4 also isn't an irrational number on its own. Like 3, 4 just ends at 4.0. Unlike 3, it's not a prime number. In addition to 1 and 4 being its factors, 2 is also a factor. So you can get 4 by multiplying (1*4), (4*1), and (2*2).

You can, however, make 3 and 4 irrational numbers. Take the square root of 3, and you'll have a continuous chain of numbers occurring after the decimal. It would equate to 1.73205081...etc. The square root of 4 is just 2, and is therefore not an irrational number. Take the cubed root instead, giving 1.58740105...etc.

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