Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Prove that for any distinct primes $p$ and $q$ , the ratio $\frac{\sqrt{p}}{\sqrt{q}}$ is irrational.

Patatiniuh 2022-07-15

Prove: every irrational number $q$ , given $e > 0$ , there exists natural numbers $N$ and $M$ such that $| N q - M | < e$

Wade Bullock 2022-07-15

Prove that if $p$ is a prime number, then $\sqrt{p}$ is an irrational number.

rmd1228887e 2022-07-15

Is there a 'far' irrational number?

Ciara Mcdaniel 2022-07-15

Why $22 / 7$ is a rational number and $π$ is irrational number?

Kaeden Hoffman 2022-07-14

Let $x > 0$ , and let $α$ be an irrational number. Can we make sense of $x^{α}$ ? What about the case $x < 0$ ?

uri2e4g 2022-07-13

For instance, let the function:
$f = \prod_{n = 1}^{\infty} \sqrt[b]{a},$
for $b \in N$ , $b > 1$ and $a$ irrational such that $f$ converges to the real number $k$ . We immediately see that all partial products are irrational. Can we then also say that $k$ is irrational?

Patatiniuh 2022-07-13

Сompute Irrational roots of the equation $y^{3} - 3 y = \sqrt{y + 2}$

Salvador Bush 2022-07-12

If we have two even numbers, say $2 m$ and $2 n$ where $m$ and $n$ are integers.
$\frac{even}{even} = \frac{2 m}{2 n} = \frac{m}{n}$
where( $\frac{m}{n}$ ) nature is still unknown. So, what nature does $\frac{even}{even}$ have, rational or irrational?

lilmoore11p8 2022-07-12

If $\cos (a) - \sin (a)$ irrational, too?

Brock Byrd 2022-07-12

Domain of ${(f (x))}^{a}$ where a is an irrational number.

2d3vljtq 2022-07-12

If $x$ and $y$ are irrational numbers then $x$ to the power of $y$ is irrational I am asked to prove or disprove this statement.

antennense 2022-07-11

Proof Irrational number $x$ , given $N \in N$ exists $ϵ > 0$ so all rationals $\in V_{ϵ} (x)$ have denominator larger than $N$ .

Frank Day 2022-07-11

How show the $\sqrt{2} \times \sqrt{2} = 2 = \frac{2}{1}$ symbolically?

EnvivyEvoxys6 2022-07-10

Prove:If $x$ is irrational, then $n x - [n x]$ are distinct for all $n \in Z$ .

Araceli Clay 2022-07-10

How notate the set of irrational numbers?

icedagecs 2022-07-09

Prove: For every rational number $x$ and every irrational number $y$ , $x y$ is irrational.

2d3vljtq 2022-07-09

Rational numbers raised to an irrational power.

vasorasy8 2022-07-09

Is it true that for any sequence of irrational numbers ${h_{n}}$ converges to zero in $[- h, h]$ both $α + h_{n} and α - h_{n}$ and $α + h_{n} and α - h_{n}$ are always irrationals ?

Callum Dudley 2022-07-09

Is real number system combination of rational and irrational numbers?

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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