Mar 13, 2005 · Assume that the difference between a rational number and an irrational number is an irrational number. The sum of any such two irrational numbers would be a rational number.

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 …

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 …

Jul 24, 2013 · Pi is irrational in any base, as its property of being rational is independent of the base used for representation. While it can be expressed differently in various bases, such as …

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 …

Jun 26, 2008 · But again, an irrational number plus a rational number is also irrational. Therefore, there is always at least one rational number between any two rational numbers. However, the …

Jul 29, 2010 · The discussion focuses on proving that irrational numbers are dense in the real numbers, starting from the established fact that rational numbers are dense in R. The initial …

Jan 6, 2012 · Homework Statement Prove If x^2 is irrational then x is irrational. I can find for example π^2 which is irrational and then π is irrational but I don't know how to approach the …

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 …

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 …