Jan 12, 2022 · A polynomial can indeed have irrational coefficients, as demonstrated by the example y = x^2 + sqrt (5)x + 1. The confusion arises from historical conventions where …

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 …

Feb 11, 2019 · ⁡ (1 ∘) is irrational. Homework Equations The Attempt at a Solution Suppose for contradiction that is rational. We claim that this implies that is rational. Here is the proof by …

Feb 23, 2012 · The discussion revolves around proving that the square root of an irrational number is also irrational. Participants suggest using proof by contradiction, where assuming …

Dec 28, 2016 · There are an infinite number of irrational numbers just as there are an infinite number of integers, rational numbers and real numbers. However since reals are uncountable …

Dec 6, 2004 · The discussion centers on the nature of irrational numbers and their existence in the physical world, questioning how lengths like the hypotenuse of a right triangle can be …

Nov 24, 2007 · Homework Statement Prove that log2 of 5 is irrational. Homework Equations None. The Attempt at a Solution I just had a glimpse of the actual solution...

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...

Feb 6, 2011 · How to prove that root n is irrational, if n is not a perfect square. Also, if n is a perfect square then how does it affect the proof.

Nov 18, 2003 · Not all irrational numbers can be expressed as infinite summations, as there are uncountably many irrational numbers but only countably many mathematical expressions. …