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 · 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 …
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 …
Proving Irrationals Are Dense in the Reals • Physics Forums
Jul 29, 2010 · Homework Statement Show that the irrational numbers are dense in R. [Hint: Use the fact that sqrt(2) is irrational.]Homework Equations Book already proved that the rationals are dense in …
Irrational numbers aren't infinite. are they? • Physics Forums
Dec 28, 2016 · Irrational numbers are not infinite; they are numbers that cannot be measured precisely, with only infinite decimal approximations available. For instance, 1.41421... serves as an …