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.Com
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)   (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)   (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.
RELATED QUESTIONS

Determine if the following real number is both composite and rational, both prime and... (answered by edjones)
a number cannot belong to both the rational numbers and the real numbers.? is this true... (answered by richwmiller)
Write each given statement in symbolic form and indicate its truth value. Write only your (answered by ikleyn)
Determine whether the following number is rational, irrational, or not a real number. If... (answered by Fombitz)
Determine if this is rational or irrational: sqrt 77 This would be rational... (answered by stanbon)
Determine if sqrt 77 and sqrt(-)are irrational or rational. I said that 77 was... (answered by stanbon)
is the number 0.686868... rational or irrational or both or neither? (answered by josgarithmetic)
what classification does 9.5 fall under---real, rational, integer, whole, irrational? I... (answered by tommyt3rd)
Give an example of a rational function that is undefined at x = a where a is a real... (answered by solver91311)