Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Give a concrete sequence of rationals which converges to an irrational number and vice versa.

Ayanna Trujillo 2022-06-16

Prove that for every rational number z and every irrational number x, there exists a unique irrational number such that $x + y = z$ .

Oakey1w 2022-06-16

Proof: $\sqrt{13}$ is irrational

kokoszzm 2022-06-15

A square root of an irrational number is always irrational?

Lucille Cummings 2022-06-15

Does every irrational number contain arbitrarily long sequences of some digit?

mravinjakag 2022-06-15

Is $b^{a^{1 / n}}$ an irrational number?

lobht98 2022-06-15

That an interval in the rationals will contain an irrational number?

Jase Howe 2022-06-15

Does there exist an irrational number $x > 2$ such that any positive integer $n$ can be written in the form $n = a_{0} + a_{1} x + a_{2} x^{2} + \dots$ , where $a_{i} \in {0, 1, \dots, 6}$ ?

Brunton39 2022-06-15

How to solve this equation for $y$ ? and is it an irrational number or a rational?
$\frac{2}{7} π^{2} \log 2 + \frac{16}{7} \int_{0}^{\frac{π}{2}} x \log (\sin x) d x - \sqrt{y} π^{3} = 0.$

Eden Solomon 2022-06-15

If $a . b . c, d$ are rationals and $x$ is irrational number, then prove that $\frac{a x + b}{c x + d}$ is usually a irrational number. When do exceptions occur?

Winigefx 2022-06-14

Why are there infinitely many values if a complex number is raised to an irrational power?

Dayami Rose 2022-06-14

How can exactly visualize an irrational number?

Brenden Tran 2022-06-14

We know that "a" is a Irrational number .But "a2+a" is Rational. Can You find "a"?

Erin Lozano 2022-06-14

Is a an integer to the power of an irrational number irrational?

preityk7t 2022-06-14

Prove that if $a + b$ is an irrational number, then at least one of $a$ or $b$ is irrational.

Bailee Short 2022-06-13

Can the probability of an event be an irrational number?

Makayla Boyd 2022-06-13

Proving that for each prime number $p$ , the number $\sqrt{p}$ is irrational.

telegrafyx 2022-06-13

Suppose $α$ is an irrational number, and if $f (x) = a x + b, a, b \in Z$ and that $f (α) \neq 0$ , prove that $a b \neq 0.$ .

Dania Mueller 2022-06-13

Since there is a rational number between any two irrational numbers, so can we say that rational number and irrational number have the same cardinality?

Jase Howe 2022-06-13

By using piegonhole principal, prove that for any positive irrational number $r$ and positive real numbers $x, y \in (0, 1)$ , $x < y$ , there exists a positive integer $n$ such that $x \leq n r - [n r] \leq y$ , where $[n r]$ is the integral part of $n r$ .

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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