Measuring the quantity of SQRT(2) kg with a scale is fundamentally impossible due to the inherent limitations of measurement accuracy, not because SQRT(2) is an irrational number. The discussion emphasizes that any measurement has a margin of error, which applies universally to all quantities. Participants suggest constructing a square with side lengths equal to a chosen unit to create an object with a diagonal length of SQRT(2), but this method still faces challenges related to construction errors and thermal fluctuations. Ultimately, the consensus is that while approximations can be made, precise measurement of SQRT(2) kg is unattainable.
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It's impossible, but not because the number is irrational. To what accuracy do you propose that this measurement be made? Any measurement is impossible to make beyond a given accuracy.littlemathquark said:Because of ##\sqrt{2}## be a irational numbers I think it is impossible and there is no scales that can measure irational quantity. May be approximately. But 2 kg can be measurable. İt is my efforts and thougts.
I repeat, to what accuracy?pines-demon said:I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of ##\sqrt{2}## units.
As good as your square is. If you make it really straight, thermal fluctuations may average any irregularity out.kuruman said:I repeat, to what accuracy?
If it's impossible for ##\sqrt 2##, then it's impossible for any number. Every measurement has a margin of error.kuruman said:It's impossible, but not because the number is irrational. To what accuracy do you propose that this measurement be made? Any measurement is impossible to make beyond a given accuracy.
I don't see why not. You use your trick to get a length of ##\sqrt 2## and then use that on a scale.pines-demon said:Edit: What you are not allowed to do is take a regular scale and try to find ##\sqrt{2}## units in that scale.
No it doesn’t. You have an object that is ##\sqrt 2## units within the errors of your construction.pines-demon said:I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of ##\sqrt{2}## units.
On the contrary. Thermal fluctuations add to the construction error.pines-demon said:As good as your square is. If you make it really straight, thermal fluctuations may average any irregularity out.
obviously…PeroK said:If it's impossible for ##\sqrt 2##, then it's impossible for any number. Every measurement has a margin of error.
There is also thermal expansion.Orodruin said:On the contrary. Thermal fluctuations add to the construction error.