Prove that sqrt(2) + sqrt(3) Cannot be a Rational Number

preview_player
Показать описание
Prove that sqrt(2) + sqrt(3) Cannot be a Rational Number

If you enjoyed this video please consider liking, sharing, and subscribing.

There are several ways that you can help support my channel:)

************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course

Advanced Calculus Course

Calculus 1 Course

Calculus 2 Course

Calculus 3 Course

Calculus Integration Insanity

Differential Equations Course

College Algebra Course

How to Write Proofs with Sets Course

How to Write Proofs with Functions Course

Statistics with StatCrunch Course

Math Graduate Programs, Applying, Advice, Motivation

Daily Devotionals for Motivation with The Math Sorcerer

Thank you:)
  1. The Math Sorcerer
  2. prove that the number is not rational
  3. prove it is irrational
  4. Prove that sqrt(2) sqrt(3) Cannot be a Rational Number
  5. prove irrational
  6. irrational proof
Рекомендации по теме
Prove that sqrt(2) 0:05:34

Prove that sqrt(2) + sqrt(3) Cannot be a Rational Number

Prove that sqrt(2) 0:03:51

Prove that sqrt(2) + sqrt(3) is irrational [ILIEKMATHPHYSICS]

Prove that root2+root3 0:02:09

Prove that root2+root3 is irrational-Real numbers-Class10

Simplifying sqrt(2+sqrt(3)) 0:05:31

Simplifying sqrt(2+sqrt(3))

A Proof That 0:17:22

A Proof That The Square Root of Two Is Irrational

Proof: Square Root 0:04:02

Proof: Square Root of 2 is Irrational

Prove that `sqrt(2)+sqrt(3)` 0:02:00

Prove that `sqrt(2)+sqrt(3)` is irrational.

Proof: Sqrt(3) - 0:07:53

Proof: Sqrt(3) - Sqrt(2) Irrational

Ex. N96 (who 0:18:43

Ex. N96 (who wants 7). Complex numbers. IB AA HL Maths Tutor Online.

Irrational Root 2! 0:00:59

Irrational Root 2!

Prove that root 0:07:29

Prove that root 2 + root 3 is irrational.

Prove that root 0:03:51

Prove that root 2 + root 3 is Irrational

Proof: Square Root 0:06:13

Proof: Square Root of 3 is Irrational

Root Two is 0:01:00

Root Two is Irrational Visually

Prove that root 0:00:16

Prove that root 2 Is a rational number #solutions #realnumbers

Proof that Square 0:06:56

Proof that Square Root 2 is Irrational

Proof: √3 + 0:18:57

Proof: √3 + √2 is irrational

Proof that square 0:07:47

Proof that square root of 2 is irrational | Algebra I | Khan Academy

Visual irrationality proofs 0:04:40

Visual irrationality proofs from the carpets theorem (root 2 and root 3)

Prove that 2 0:03:39

Prove that 2 root 3 is irrational number.||CBSE 2020||

Prove that 2 0:04:49

Prove that 2 + root 3 is irrational

Proving root 2 0:00:51

Proving root 2 is Irrational- Proof by Contradiction

Proving root 2 0:00:37

Proving root 2 is irrational

'Show that `2-sqrt(3)`is 0:02:52

'Show that `2-sqrt(3)`is an irrational number.'

Комментарии
Автор

Rational Roots theorem is a saviour. It makes life so much easier than showing it the manual way. Before I watched the video, I kinda expected that you would prove it by contradiction as one would normally do whenever a problem involves the word "CANNOT". Sometimes pure math is a matter of knowing as many theorems as possible and having the ability to coherently apply them.

albieadao
Автор

Assume sqrt2 + sqrt3 is rational, then it can be written as p/q where p and q share no common factors. Then consider

(sqrt2 + sqrt3)^2 = p^2 / q^2
2 + 2sqrt(6) + 3 = p^2 / q^2
<=> sqrt(6) = (p^2/q^2 - 5)/2. This is still a rational number, so we can write it as a/b where a and b share no common factors.

However, this would imply that 6b^2 = a^2, which would imply that a^2 is divisible by 3, and consequently we can write a as 9k^2, and 2b^2 = 3k^2. However, this would by the same argument imply that b is also divisible by 3. This is a contradiction.

thecactus
Автор

Please let me know if you have any questions.

vicheakeng
Автор

i love this proof! Can't you also prove that sqrt2 is irrational by applying rational roots theorem to x^2-2=0 ??

nicholasroberts
Автор

I use math for gambling just like I've beaten walkl st too. It doesn't matter what age u learn math but it has real applications out gere

johnbatchler
Автор

Most of my math skills came out if wall st

johnbatchler
Автор

U only need two yrs of math not four or higher

johnbatchler