irrational = rational - Physics Forums
Mar 13, 2005 · Explore examples of irrational numbers that can be expressed as non-repeating decimals Investigate the implications of probability in selecting random real numbers Mathematicians, students …
Is Dividing an Irrational Number by a Rational Number Always …
Nov 10, 2025 · Dividing an irrational number by a nonzero rational number results in an irrational number. The proof by contradiction assumes that the result is rational, leading to the conclusion that …
Is the square root of a prime number always going to be irrational?
Sep 2, 2006 · In general, I think that the nth root of any natural number that is not itself a perfect nth power is an irrational number. This is true, and in fact the nth root of any rational number which …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · The discussion centers on proving that is irrational through a proof by contradiction and mathematical induction. It establishes that if is rational, then must also be rational for all natural …
How Do We Know If Irrational or Transcendental Numbers Repeat?
Mar 25, 2014 · The discussion centers on the nature of irrational and transcendental numbers, specifically whether they can have repeating decimal expansions. It is established that numbers like …
Constructing Lengths with Irrational Numbers - Physics Forums
Dec 6, 2004 · Irrational numbers are just an inconsistent fabrication of abstract mathematics. Irrational lengths can't exist in the real world. And rational lengths can ? There is no way that you are going to …
Prove or disprove that there is a rational number x and an i
Jan 25, 2019 · The discussion centers on proving or disproving the existence of a rational number x and an irrational number y such that x^y is irrational. Participants suggest that proof by contradiction is a …
How did the Greeks deal with sqrt(2)? • Physics Forums
Dec 21, 2018 · The Greeks recognized the existence of irrational numbers, such as √2, but struggled with their implications due to their philosophical beliefs that all numbers should be expressible as …
Is the Square Root of Pi Irrational? • Physics Forums
Dec 14, 2012 · The discussion centers on the proof of the irrationality of the square root of pi (√π). The proof begins by assuming that √π is rational, expressed as √π = p/q, where p and q are integers. …
Is sqrt(5) Rational? Understanding the Proof by Contradiction
Nov 23, 2003 · Alright, heading says it all. This is a nice problem heh.. I can see how to prove sqrt(5) is irrational. I think this method works up to the points where the fact 5 is a prime is used, (ie prime …