Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Calculate the exact value $f l o o r (π^{k})$ without actually calculating the huge value of $π^{k}$ .

Jameson Lucero 2022-07-08

Let $A \subset R$ be a measurable and bounded and $l_{1} (A) > 0$ . Show that there exist $a, b \in A$ that $a - b$ is irrational number.

sebadillab0 2022-07-08

If I would draw a right triangle with legs of length 1 centimeter with a ruler then its hypotenuse should be equal to $\sqrt{2}$ which is an irrational number - therefore its decimal representation, which is the limit of the sequence $lim_{n \to \infty} \sum_{i = 0}^{\infty} \frac{a_{i}}{10^{i}}$ , has infinitely many numbers after the interger part of $\sqrt{2}$ .
What exactly can the ruler measure when drawing such a triangle, considering the fact that we draw irrational number (which by definition is infinitely long)?

Keenan Santos 2022-07-08

Is this proposition $\sqrt{2}$ + $\sqrt{3}$ is an irrational number." true or false?

Raul Walker 2022-07-08

Calculate the difference between π/4 and the Leibniz series for computing $π / 4$ with $n = 200$ .
This series appears to converge relatively slowly, and so at what point can we confidently say that "the $576$ th digit is $3$ " of an irrational number?

Patatiniuh 2022-07-07

How to find out any digit of any irrational number?

Lorena Beard 2022-07-07

Is there a proof that $π$ is an irrational number?

Sonia Ayers 2022-07-07

Let $f : R \to R$ be a function such that for any irrational number $r$ , and any real number $x$ we have $f (x) = f (x + r)$ . Show that f is a constant function.

Maliyah Robles 2022-07-07

Construct an increasing function $f$ on $R$ that is continuous at every irrational number and is discontinuous at every rational number.
Solution: Let $r_{n}$ be a sequence with distinct terms whose range is $Q$ . Let $f : R \to R$ be given by
$f (x) = \sum_{r_{n} < x} \frac{1}{2^{n}}$

Banguizb 2022-07-07

Calculate the quadratic irrational number $α$ given by the periodic continued fraction $α = \bar{[1, 2, 1]}$ .

ntaraxq 2022-07-06

cos $\cos (A π)$ where $A$ is an irrational algebraic number

pouzdrotf 2022-07-06

Prove that $\sqrt{47}$ is irrational number.

Sylvia Byrd 2022-07-06

Proving Is mth root of $2$ an irrational number for every integer $m \geq 2$

racodelitusmn 2022-07-06

Lets say we have irrational numbers $α_{1}, . . ., α_{n}$ in the interval $(0, 1)$ . Represent each αi as a binary expansion $0. a_{i}^{1} a_{i}^{2} . . .$ where each a $a_{i}^{j} \in {0, 1}$ . Define the "dovetail" of the $α_{i}$ to be the number with binary expansion $0. a_{1}^{1} a_{2}^{1} a_{3}^{1} . . . a_{n}^{1} a_{1}^{2} a_{2}^{2} a_{3}^{2} . . . a_{n}^{2} a_{1}^{3} a_{2}^{3} a_{3}^{3} . . .$
So that the dovetail is irrational?

Patatiniuh 2022-07-06

Using the fact that $\sqrt{n}$ is an irrational number whenever $n$ is not a perfect square, show 3 $\sqrt{3} + \sqrt{7} + \sqrt{21}$ is irrational.

prirodnogbk 2022-07-06

Can any two irrational numbers NOT of the form $(m + A)$ and $(n - A)$ be added to produce a rational number?

Wronsonia8g 2022-07-04

Is there a real number $r$ such that all $r^{n}$ are irrational for all integers $n \geq 1$ but it is not transcendental?

Cierra Castillo 2022-07-04

How to construct a rational number sequence for any irrational number

Carly Cannon 2022-07-04

For every irrational number $i_{1} \in [0, 1]$ , there is only one irrational number $i_{2} \in [0, 1]$ such that $i_{1} - i_{2} \in Q$ ?

dream13rxs 2022-07-04

Proof that $\log_{2} 3 + \log_{5} 2$ 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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