Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Prove that between any two rational numbers, there are two irrational numbers whose difference is rational

Cael Dickerson 2022-11-11

Proof that the set of irrational numbers is uncountable?

Sophie Marks 2022-11-11

Proved or disproved: Any irrational number without a $0$ (zero) in its decimal representation is transcendental.

Jenny Schroeder 2022-11-11

Let $a - b$ be an irrational number where $a, b > R_{+}$ . What can be said about $a$ and $b$ ?

Paula Cameron 2022-11-11

Prove that among $2 n + 1$ irrational numbers we can choose $n + 1$ numbers such that the sum of any two chosen numbers is irrational.

ajumbaretu 2022-11-11

Prove that this sum of two irrational numbers is rational number
$\sqrt[3]{2 - \sqrt{5}} + \sqrt[3]{2 + \sqrt{5}}$

Kaylynn Cook 2022-11-10

Let $x$ and $y$ be real numbers. If $xy$ is irrational, then $x$ is irrational or $y$ is irrational

spasiocuo43 2022-11-09

Why differentiate between irrational and transcedental numbers?

spasiocuo43 2022-11-09

Explanation why irrationals are uncountable? I am a beginner and any help would be greatly appreciated.

Joglxym 2022-11-08

Rational and irrational numbers under base pi

Emmanuel Giles 2022-11-08

Let $f : R \to R$ be a continuous map such as each irrational number is mapped to a rational number (i.e. $f (R ∖ Q) \subset Q$ ). Show that $f$ is a constant map.

Howard Nelson 2022-11-06

What is the probability that a random number is irrational/transcendental? Are there infinitely more transcendental numbers than irrational numbers?

fabler107 2022-11-06

Show that:
If $x$ is an real number, there is a sequence of irrational numbers converging to $x$ .

Jaiden Elliott 2022-11-06

Why the set of irrational numbers is represented as $R ∖ Q$ instead of $R ∖ Q$ ?

Layton Park 2022-11-06

How to/Can we show irrational numbers?

Leanna Jennings 2022-11-06

What is an example of a function $f : R \to R$ that is only continuous on the irrational numbers and zero?

Jorge Schmitt 2022-11-06

Find all solutions in un-ordered integers $(a, b)$ to $7 - a - b = 2 \sqrt{10} - 2 \sqrt{a b}$

kaltEvallwsr 2022-11-06

Prove "If x and y are irrational numbers, then $3 x + 4 x y + 2 y$ is irrational"

clealtAfforcewug 2022-11-05

Suppose $a, b$ are two irrational numbers such that ab is rational and $a + b$ is rational. Then $a, b$ are the solution to a quadratic polynomial with integer coeffecients.

Layton Park 2022-11-05

Show that the set of irrational numbers fails to be closed

The use of irrational numbers is quite common for the Engineering disciplines where various irrational numbers equations are used to determine the rightfulness of some calculations or tasks that require prognosis. As a way to make things easier, you can take a look at the list of questions related to irrational numbers and receive immediate help as you look through the list of answers.

If you need additional assistance or feel unsure about your task, simply compare these examples with your task and proceed from there.

Algebra I

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