Is The Product Of Two Irrational Numbers Always Irrational, Sum And Product Rationals Irrationals

But it turns out that books disproves the statement saying $sqrt2cdotsqrt2=2$ which is a rational number and hence Product of two irrational number need not always be irrational. Which I find convincing.

Đang xem: Is the product of two irrational numbers always irrational

Can someone please point out where am I going wrong in my proof?

discrete-wtbblue.comematics logic propositional-calculus irrational-numbers
Share
Cite
Follow
edited Jan 11 “15 at 17:35

*

Martin Sleziak
52.3k1616 gold badges155155 silver badges312312 bronze badges
asked Sep 25 “13 at 4:48

*

Amit TomarAmit Tomar
35333 gold badges55 silver badges1313 bronze badges
$endgroup$
13
1
$egingroup$ The contrapositive is $
eg q implies
eg p$. $endgroup$–user61527 Sep 25 “13 at 4:50

| Show 8 more comments

3 Answers 3

Active Oldest Votes
3
$egingroup$
The negation of the assertion <Is the product of two irrational numbers> is the assertion <Is not the product of two irrational numbers>. There is no a priori reason to expect that the assertion <Is not the product of two irrational numbers> is equivalent to the assertion <Is the product of two rational numbers> (and in fact these last two are not equivalent).

Read more: The Meaning Of Patriotism Is The Virtue Of The Vicious ? Patriotism Is The Virtue Of The Vicious

Share
Cite
Follow
edited Sep 25 “13 at 8:03
answered Sep 25 “13 at 5:27

*

DidDid
265k2626 gold badges266266 silver badges523523 bronze badges
$endgroup$
Add a comment |
2
$egingroup$
Disprove:

Let $sqrt{2}$ be the irrational number. Then $sqrt{2} imes sqrt{2}=|2|$, which is rational. So, the product of two irrational numbers is not always irrational

Share
Cite
Follow
answered Sep 28 “14 at 6:57

*

Hassan MuhammadHassan Muhammad
3,68033 gold badges2929 silver badges4646 bronze badges
$endgroup$
2
Add a comment |
1
$egingroup$
Some more examples are

$$sqrt{8}×sqrt2=sqrt{16} =4$$

$$sqrt2×sqrt{32}=sqrt{64} =8$$

$$sqrt5×sqrt5=sqrt{25} =5$$

In this way product of two irrational number is rational.

Read more: Wow Wow Wubbzy Dvd Menu Walkthroughs: Wow Wow Wubbzy, Dvd Menu Walkthroughs: Wow Wow Wubbzy

Share
Cite
Follow
edited Jul 25 “15 at 18:26

*

Peter Woolfitt
20.4k66 gold badges4848 silver badges8484 bronze badges
answered Jul 25 “15 at 17:59
shrutishruti
1122 bronze badges
$endgroup$
1
Add a comment |
Highly active question. Earn 10 reputation in order to answer this question. The reputation requirement helps protect this question from spam and non-answer activity.

Not the answer you're looking for? Browse other questions tagged discrete-wtbblue.comematics logic propositional-calculus irrational-numbers or ask your own question.

Featured on Meta
Linked
8
How to show that the product of two irrational numbers may be irrational?
Related
6
sum of irrational numbers – are there nontrivial examples?
1
Check if this proof about real numbers with an irrational product is correct.
0
Contradiction proof of the product of two irrational numbers
2
Proving either $x^2$ or $x^3$ is irrational if $x$ is irrational
2
Prove that there is an irrational number and a rational number between any two distinct real numbers
0
What's the error in my proof of the statement: The product of two irrational numbers is irrational?
0
Problem with formulating the negation of a statement
0
Evaluating a simple proof about rational numbers
5
Axiom to prove $ sqrt2 $ is irrational by contradiction.
Hot Network Questions more hot questions
Question feed
Subscribe to RSS
Question feed To subscribe to this RSS feed, copy and paste this URL into your RSS reader.

wtbblue.comematics
Company
Stack Exchange Network
site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.4.26.39152

wtbblue.comematics Stack Exchange works best with JavaScript enabled

*

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.

Leave a Comment