SOLUTION: Determine if the following real number is both composite and rational, both prime and rational, only rational or only irrational. PIE ; like 3.14159265359

Algebra ->  Real-numbers -> SOLUTION: Determine if the following real number is both composite and rational, both prime and rational, only rational or only irrational. PIE ; like 3.14159265359      Log On


   

Question 465348: Determine if the following real number is both composite and rational, both prime and rational, only rational or only irrational.
PIE ; like 3.14159265359
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


There are no two integers such that is equal to the quotient of those two integers.



Therefore:



In other words, is irrational.

Furthermore:

There is no polynomial equation with rational coefficients such that is a root. Therefore is trancendental, which is to say:



Where is the set of all real numbers that are roots of polynomial equations with rational coefficients.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The number is obviously neither composite nor prime (those words are reserved for integers only), and pi is not a rational number. It is only irrational, and like the other tutor said, it is transcendental, meaning it cannot be the root of any polynomial with rational coefficients.