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 …
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 …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · Homework Statement Prove that tan (1 ∘) is irrational. Homework Equations The Attempt at a Solution Suppose for contradiction that is rational. We claim that this implies that is rational. …
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 …
Proving Irrationals Are Dense in the Reals • Physics Forums
Jul 29, 2010 · The discussion focuses on proving that irrational numbers are dense in the real numbers (R). The proof utilizes the property that the sum of a rational number and an irrational number is …
Proving the area formula for a rectangle for all positive real numbers ...
Aug 3, 2024 · The area formula for a rectangle, defined as length times width, holds true for all positive real numbers, including rational and irrational values. The discussion emphasizes the need for an …
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 …
Is Pi a rational number in any other base besides base Pi?
Jul 24, 2013 · So is an irrational number always irrational no matter what the base or is Pi just a special case? The term "irrational" is independent of what base we use. So yes, an irrational number is …
How Can Rational and Irrational Numbers Combine in Arithmetic ...
May 14, 2017 · This discussion focuses on the arithmetic operations involving irrational numbers, specifically how certain combinations can yield rational or irrational results. Examples provided …
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. …