Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Prove or disprove that there is a rational number $x$ and an irrational number $y$ such that $x^{y}$ is irrational.

Brooke Ayala 2022-05-19

Can Arg( $ν$ ) be of the form $π \times μ$ for an irrational number $μ$ ?

istremage8o 2022-05-19

Proof of $π$ not being a quadratic irrational number.

Chaz Blair 2022-05-19

Let $a \in (0, 1)$ be an irrational number and suppose there exists a sequence
$r_{n} = \frac{p_{n}}{q_{n}}$ with $p_{n}$ , $q_{n} \in N$ and $lim_{n \to \infty} r_{n} = a$ .
Show that both ${p_{n} : n \in N}$ and ${q_{n} : n \in N}$ are not bounded.
Suppose $a \notin Q, a \in (0, 1),$ and sequence $r_{n} = \frac{p_{n}}{q_{n}} \to a$ , with $p_{n}, q_{n} \in N$ . Show that both ${p_{n} : n \in N}, {q_{n} : n \in N}$ are not bounded.

herbariak1 2022-05-19

Raising a negative real base to an irrational number.
Example:
$y = (- 2)^{π}$

Riley Yates 2022-05-18

For an irrational number $α$ , prove that the set ${a + b α : a, b \in Z}$ is dense in $R$ .

Zeihergp 2022-05-18

Prove $2^{1 / 3}$ is irrational.

Aditya Erickson 2022-05-18

Show that an irrational number $ξ = [a_{0}; a_{1}, \dots]$ has bounded partial quotients $a_{k}$ if and only if there exists $δ > 0$ such that
$| ξ - \frac{p}{q} | > \frac{δ}{q^{2}}$
for all rational $\frac{p}{q}$ .

Brennen Fisher 2022-05-18

Suppose we take all the rationals and take any neighbourhood around each of them. Will they cover whole $R$ . Rationals are dense. So, for each irrational we can find a rational which is arbitrary close to it. Is it correct ?

Kazeljkaml5n9y 2022-05-17

Suppose $\sqrt{2}$ is an irrational number and $0$ is a rational number. Because
$\sqrt{2} = \sqrt{2} + 0$
the sum of an irrational number and a rational number is an irrational number.
Is this correct?

Dominick Blanchard 2022-05-16

It is known that constants $π$ and $e$ are irrational numbers but also transcedental.Where consist difference between irrationality and transcedentality. How we know that given irrational number is not tanscedental?

vulkanere64t6 2022-05-16

Prove that $\sqrt{3} + \sqrt{5}$ is an irrational number.

anniferathonniz8km 2022-05-15

Proof there is an irrational number $r$ in every intervall $a < r < b$ .

garcialdaria2zky1 2022-05-15

Prove that there is an irrational number between any two unequal rational numbers a,b.

sembuang711q6 2022-05-15

How can I prove that the sum of two irrational numbers is most likely irrational number?

zuzogiecwu 2022-05-15

Find an irrational number whose binary development does not contain strings of $0$ s or $1$ s of arbitrary length

Alisa Durham 2022-05-15

Is ${({({(\sqrt{2})}^{\sqrt{2}})}^{\sqrt{2}})}^{\dots}$ an irrational number?

Ainsley Zimmerman 2022-05-14

Prove if $n$ is an irrational number then $- n$ is so.

deformere692qr 2022-05-14

What irrational number has the simplest calculation in terms of computation?

Jayden Mckay 2022-05-14

Prove that $\sqrt{\frac{3}{5}}$ is irrational number.

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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