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 …
irrational = rational - Physics Forums
Mar 13, 2005 · Can someone prove that there exists x and y which are elements of the reals such that x and y are irrational but x+y is rational? Certainly, there are an infinite number of examples (pi/4 + …
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 …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · Homework Statement Prove that ##\tan (1^\circ)## is irrational. Homework EquationsThe Attempt at a Solution Suppose for contradiction that ##\tan...
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 …
Proof that sqrt(6)-sqrt(2)-sqrt(3) is irrational - Physics Forums
Mar 21, 2008 · The discussion focuses on proving that the expression √6 - √2 - √3 is irrational without using polynomials or the rational root theorem. Participants explore various approaches, including …
Sequence of rationals converging to an irrational limit
Aug 23, 2009 · As another illustration, I understand that if a sequence (s_n) given as s_n = \sqrt {2} + 1/n is a sequence of IRRATIONAL numbers converging to an IRRATIONAL limit.
How Are Rational and Irrational Numbers Distributed Along the Real …
Oct 30, 2011 · Hey. I've been wondering, from -infinity to positive infinity, what does the distribution of rational vs. irrational numbers look like? Are there any notable or interesting patters/points to make …