Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Does there exist an irrational number $x$ and an integer sequence $(a_{n})$ such that
$lim_{n \to \infty} | a_{n} - n! x | = 0.$

Hailee Stout 2022-05-13

Why can't imaginary numbers be irrational?

Alexis Meyer 2022-05-13

Do irrational number contain infinite/every patterns of sequences?

Matthew Hubbard 2022-05-13

Is $z = \sqrt{\frac{\sqrt{3 x + 1}}{\sqrt{3 x - 1}}}$ a rational or irrational number?

jistefaftexia99kq6 2022-05-12

How to prove that a $0.1234567891011121314...$ is irrational?

Waylon Mcbride 2022-05-12

Prove that $2^{\sqrt{3}}$ is irrational or even it is transcendental?

Daphne Haney 2022-05-12

why measure of irrational number intersect [0,1] is 1?

Waylon Mcbride 2022-04-12

How can we get Nth digit of any irrational number in base $2$ using Taylor expansion?

agrejas0hxpx 2022-04-10

Just as $ℑ (z)$ ) and $ℜ (z)$ denote the imaginary and real parts of $z$ , respectively, do there exist symbols for the rational and irrational parts of a real number?

rynosluv101wopds 2022-04-10

In the range of $[0, 1] \in R$ , construct a series which is strictly increasing and rational number and irrational numbers are alternatively appearing.

oglasnak9h01 2022-04-10

Can you raise the imaginary number i to a power that is an irrational number?

In which set(s) of numbers would you find the number-79

aramutselv 2022-01-06

$\sqrt[31]{12} + \sqrt[12]{31}$ is irrational?

oliviayychengwh 2022-01-06

Can an irrational number raised to an irrational power be rational?
If it can be rational, how can one prove it?

Helen Lewis 2022-01-05

Expansion of ${(1 + \sqrt{2})}^{n}$
I was asked to show that $\forall n \in N$ there exist a $p \in N^{\cdot}$ such that
${(1 + \sqrt{2})}^{n} = \sqrt{p} + \sqrt{p - 1}$
I used induction but it wasn't fruitful, so I tried to use the binomial expansion of ${(1 + \sqrt{2})}^{n}$ but it seems I lack some insight to go further.
Any hint is welcomed.

kerrum75 2021-12-29

How do you find the principal square root of 8?

jamessinatraaa 2021-12-26

How do you simplify 1 over square root 2?

jamessinatraaa 2021-12-22

How do you find the square root of 81?

bmgf3m 2021-12-18

How do you simplify: square root of 20?

Madeline Lott 2021-12-17

What is the square root of 24?

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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