Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Can every irrational number be written in terms of finitely many rational numbers?

Kassandra Ross 2022-06-13

How to use the Lemma of Heine–Borel in order to prove the existence of an irrational number?

boloman0z 2022-06-12

Find a sequence of rationals that converges to arbitrary irrational number $β$ .

Semaj Christian 2022-06-12

How prove that any number to be irrational?

misurrosne 2022-06-10

Prove that 2.101001000100001... is an irrational number.

Amber Quinn 2022-06-10

What's between an irrational and rational number?

Emmy Dillon 2022-06-10

Why arccos $\arccos (\frac{1}{3})$ is an irrational number?

juanberrio8a 2022-06-09

Is $\frac{1}{11} + \frac{1}{111} + \frac{1}{1111} + \dots$ an irrational number?

manierato5h 2022-06-09

Prove the following statement by proving its contrapositive: if $r$ is irrational, then $r^{\frac{1}{5}}$ is irrational.

Davion Harding 2022-06-08

$(\forall x \in I^{+}) [\sqrt{x} \in I]$ where $I^{+}$ represents the domain of all positive irrational numbers.
Write it as a universal generalization proof.

glycleWogry 2022-06-07

How to prove that the power $b^{n}$ is an irrational number, where $b$ is an integer greater than $1$ and $n$ is an irrational number?

Roland Waters 2022-06-06

Is irrational number set on $R$ disconnected?

Jaqueline Kirby 2022-06-06

Prove that the square root of a Mersenne number ( $k = 2^{n} - 1$ ) is irrational.

gnatopoditw 2022-06-05

Show that $(lim x_{n})^{2} = a$ and thus exhibit the existence of a positive square root of $a$ . (because we took $x_{1} > 0$ )

rigliztetbf 2022-06-05

Prove that the { fractional part of $n α ∣ n \in N$ } is dense in $[0, 1]$ for an irrational number $α$ .

Yahir Tucker 2022-06-05

In what connection have to be rational parameters and irrational number for $\frac{a x + b}{c x + d}$ to be rational number?

Erin Lozano 2022-06-05

Is this : $\sqrt{3 + \sqrt{2 + \sqrt{3 + \sqrt{2 + \sqrt{\dots}}}}}$ irrational number?

pastissonv185x 2022-06-04

$p_{n} / q_{n}$ (where $p < n$ and $q_{n}$ are sequences over the naturals $N$ ). If the limit of an (when $n$ diverges (to infinity)) is $r$ which is an irrational number :
$lim a_{n} = r | r \in R ∖ Q$
Does that $p_{n}$ and $q_{n}$ both diverge (to infinity)?

mllewestblam2 2022-06-04

How many representations are possible of an irrational number?

Kubjatkocn2cl 2022-06-04

If $x^{(1 / 3)}$ is an irrational number, then $x$ is also irrational.

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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