Number in front of square root

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hashimtmahmood

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Hi, I'm unsure if this is in the right thread, if not I apologise. I have an equation attached that I'm unable to solve, could you please provide explain what the 12 does to the square root of 1.1268 to make it equal 1.01? Thanks.
 

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Hi, I'm unsure if this is in the correct thread, if not I apologise. I have attached an equation, where I am unsure what exactly the 12 does to the square root of 1.1268 to equal 1.01? Any help would be appreciated. Thanks.
 
It looks like a misprint. It should say, [MATH]\sqrt[12]{1.1268} = 1.01[/MATH], which is correct (the 12th root). I have never seen a notation in which the index of a radical is written as a pre-subscript.
 
[math] \sqrt{x} = x^{\frac{1}{2}} [/math]
[math] \sqrt[12]{x} = x^{\frac{1}{12}} [/math]
 
And, again, the 12 doesn't do anything to the "square root" of 1.1268 because there is NO square root! The 12th root of 1.1268, \(\displaystyle \sqrt[12]{1.1268}\), is (using the "\(\displaystyle \sqrt[y]{x}\)" key on the calculator that comes with windows) 1.009998130389220763765656635921 which rounds to 1.01.
 
HallsofIvy said:
And, again, the 12 doesn't do anything to the "square root" of 1.1268 because there is NO square root! The 12th root of 1.1268, \(\displaystyle \sqrt[12]{1.1268}\), is (using the "\(\displaystyle \sqrt[y]{x}\)" key on the calculator that comes with windows) 1.009998130389220763765656635921 which rounds to 1.01.
Click to expand...
But it is the sixth-root of the square-root!! - like cousin sixth-removed...... there is undeniable blood-line....
 
It may be worth pointing out that as written, it actually looked more like [MATH]12^{\sqrt{1.1268}} = 13.98[/MATH]. So it did make sense to have asked what the 12 does to what appears, as written, to be a square root!

Or has anyone seen this notation actually used for a 12th root?
 
[math] _{12}\sqrt{x} [/math] is actually a common operator that means:- take the square-square-cube root of x and round to 3 significant figures. I'm surprised no-one has seen this before ;)
 
Cubist said:
[math] _{12}\sqrt{x} [/math] is actually a common operator that means:- take the square-square-cube root of x and round to 3 significant figures. I'm surprised no-one has seen this before
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Cubist, please give us a reference where one might find that notation.
Also tell us what 'square-square-cube root of x ' means.
 
pka said:
Cubist, please give us a reference where one might find that notation.
Also tell us what 'square-square-cube root of x ' means.
Click to expand...

My comment was purely a joke - thus the winky face. I guess that tutors who see this kind of thing regularly would not find this funny so please accept my appology!

Being serious - I think that the author of OP's question probably just made a simple LaTeX error, not knowing that "\sqrt[n]{x}" is the proper way to get [math] \sqrt[n]{x} [/math]. It seems pretty certain, to me, that 12th root was intended. And the OP is probably more familiar with simple square roots rather than nth roots, thus the question.
 
I seem to recollect that Dr. Peterson has available a scolarly source on the history of mathematical notation. Just based on wikipedia, the radical symbol in its modern guise was developed by Descartes and seems to have originally been just a square root symbol. Furthermore, even today, the symbol means square root unless explicitly specified as being a higher order root. So, unlike Halls, I have no problem with LaTeX's use of \sqrt to indicate the symbol of radical plus attached vinculum. LaTeX is typographical software rather than mathematics, and I do not find it difficult to keep straight the difference between the name of a symbol and the name of the concept symbolized.

Like Halls, however, I find it it very sloppy to read "third root of x" as "third square root of x," which is literally meaningless and may be misconstrued as the cube root of the square root. Subhotosh' and cubist's jokes nicely reinforce Hall's fundamental point. Of course, in the case of the OP, this was almost certainly not sloppiness but simple lack of familiarity with the notations. So it was a good question.
 
Yes, there were various ideas for placing the index (as a number or letter) somewhere around the radical; see Cajori here. None that I see there looks like the OP, which I do think was a typo at some level. I do see a variety of notations around the world, just not this one, either past or present.
 
Thanks. Dr. Peterson.

Cautionary note. I do know how to spell "scholarly," but turned off spellcheck at this site because it plays hob with LaTeX.
 
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