Prove that the there is No Rational Number Whose Square is 2

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In this video we prove that there is no rational number whose square is 2. I hope this video is helpful.

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  1. The Math Sorcerer
  2. prove that there is no rational number whose square is 2
  3. proof
  4. prove
  5. rational number
  6. square root of 2 is irrational
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Комментарии
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Hey man, it's good that you're posting more frequently but I suggest spacing your uploads more. Instead of a few times per day make it once a day or something similar so you won't run out of ideas quickly and get more views on each video. Best of luck!

OfficalMcM
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Generalize this please? Prove that if n is a non-negative integer, then sqrt(n) is either an integer or irrational number.

deltatwo
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Thanks for this video .. it helps me to understand better than my text book

a.a
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I have two questions:
1. Why do we have to assume that our rational number is in lowest terms to prove the theorem?
2. Why proving the contradiction that our rational number is not in lowest terms (it does have a common factor between numerator and denominator) proves that there is not rational number whose square is 2?

luylasnubes
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Many thanks for the explanation.God bless you..

vishnuks
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Sir can you please upload on real analysis 1

MuhammadIsmail-unqd
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Thanks for posting these! I'm learning a lot. Sorry if these questions are stupid. Why did you impose the extra condition, that p and q are in the lowest terms, when it was not part of the original statement? If we did not impose the extra condition, wouldn't we fail to find the contradiction? Would this then mean that there is a rational number, whose square is 2?

bbrin
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In which branch of mathematics we can solve such questions ?

AIG-FFYT
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It's the definition of a Prime Number that it will have no root that is a rational number. So let's prove that 2 is a Prime Number. Okay, can we divide two by any other integer besides unitary 1 and get an integer. Nope. So the root of 2 will not be a Rational Number, or, as you would put it, there is not a Rational Number that if you squared it would equal 2.

leovolont