What is the Sum of Two Irrational Numbers? - Physics Forums
Feb 14, 2005 · I have a question. I realize that two rational numbers added together equal a rational number and that a rational added to a irrational equal a irrational number; but how do I …
Is Dividing an Irrational Number by a Rational Number Always …
Oct 13, 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 …
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 …
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 …
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...
Proof that cube roots of 2 and 3 are irrational - Physics Forums
Jul 20, 2018 · Proof by contradiction that cube root of 2 is irrational: Assume cube root of 2 is equal to a/b where a, b are integers of an improper fraction in its...
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 …
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 …
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 …
Irrational number to an irrational power • Physics Forums
Jun 13, 2013 · Homework Statement if a and b are irrational numbers, is a^b necessarily an irrational number ? prove it. The Attempt at a Solution this is an question i...