EPTI search for it on google, found a lot of hows, but not whys, can some one explain why ? Teaching some math and was doing good till a student ask me why square root of 2 can be written as 2^(1/2) and I got stuck.
WHY!?!? fractional exponents for radicals
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rei
United States3594 Posts
I search for it on google, found a lot of hows, but not whys, can some one explain why ? Teaching some math and was doing good till a student ask me why square root of 2 can be written as 2^(1/2) and I got stuck. | ||
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Seronei
Sweden991 Posts
2^(1/2) is the square root of 2 and the definition of square root is x^(1/2) | ||
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Kazius
Israel1456 Posts
2^1 * 2^(-1) = 2^(1 + (-1)) = 2^0 2^(1/2) * 2^(1/2) = 2^(1/2 + 1/2) = 2^1 | ||
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Slayer91
Ireland23335 Posts
Since the Square root of 2 is a number that is multiplied by itself to give 2, to get 2, that's the same as adding the exponents of 1/2 and 1/2 to get 2^1 Remember the law of indices? 2^1/2 + 2^1/2 = 2^(1/2 + 1/2) =2^1 It's really the definition of square root, that's why its hard to explain. | ||
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Inzek
Chile802 Posts
a*a=a^(1+1) 2^(1/2)*2^(1/2)=2 go backwards and i think you can prove something.. also finally is just notation... like dx/dy is not dx/dy | ||
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Housemd
United States1407 Posts
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xlep
Germany274 Posts
By the definition of arithmetics when using powers (hope thats the correct word) in mathematics: x^a * x^b = x^(a+b) Considering that "square root of x" * "square root of x" = x; "square roof of x" must be x^(1/2) | ||
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MangoTango
United States3670 Posts
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starfries
Canada3508 Posts
ie for x and y =/= 0 x ^ 0 = 1 0 ^ y = 0 0 ^ 0 = 1 | ||
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SirKibbleX
United States479 Posts
2^3 = 8 2^2 = 4 2^1 = 2 2^0 = 1 (Just keep dividing by 2 each time you decrement the exponent) 2^(-1) = 1/2 2^1 * 2^1 = 2^2 2^0 * 2^1 = 2^1, etc. (Exponents multiplied "sum") 2^(1/2) * 2^(1/2) = 2^1 Also remembering that exponents raised to another power 'multiply': 2^(1/2) * 2^(1/2) = [2^(1/2)]^2 = 2^1 It probably makes most sense backwards, by saying something like "What number squared would make two? That number must be two to the one-half power, because exponents 'sum' when multiplied." x^(2) = 2 => x=sqrt(2) | ||
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nalgene
Canada2153 Posts
You can use that to check ( you can also type Engrish words into it if you need to ) is he looking for something like this? 2^3/2 = Sqrt ( 2^3 ) 2^5/2 = Sqrt ( 2^5 ) 2^4/3 = CubeRoot ( 2^4 ) 2^5/4 = 4th Root( 2^5 ) | ||
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andrewlt
United States7702 Posts
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Bibdy
United States3481 Posts
On February 05 2011 03:11 SirKibbleX wrote: This is a very simple explanation: 2^3 = 8 2^2 = 4 2^1 = 2 2^0 = 1 (Just keep dividing by 2 each time you decrement the exponent) 2^(-1) = 1/2 2^1 * 2^1 = 2^2 2^0 * 2^1 = 2^1, etc. (Exponents multiplied "sum") 2^(1/2) * 2^(1/2) = 2^1 Also remembering that exponents raised to another power 'multiply': 2^(1/2) * 2^(1/2) = [2^(1/2)]^2 = 2^1 It probably makes most sense backwards, by saying something like "What number squared would make two? That number must be two to the one-half power, because exponents 'sum' when multiplied." x^(2) = 2 => x=sqrt(2) Here's your answer. Its simply logical progression. If you take the root of x (x^1/2) and square it (multiply the exponent by 2) you get x^1, as expected. | ||
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rei
United States3594 Posts
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micronesia
United States24734 Posts
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Empyrean
17014 Posts
On February 05 2011 03:00 starfries wrote: the 0 exponents blew my mind more ie for x and y =/= 0 x ^ 0 = 1 0 ^ y = 0 0 ^ 0 = 1 The last assertion is incorrect. 0^0 is an indeterminate form. | ||
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Djzapz
Canada10681 Posts
On February 05 2011 05:36 Empyrean wrote: The last assertion is incorrect. 0^0 is an indeterminate form. It still gives 1 on calculators and maple so people don't know that  | ||
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rei
United States3594 Posts
On February 05 2011 05:22 micronesia wrote: Who were you teaching math? What math? Where Why How? 10th graders, advance algebra2,Thomas Jefferson high school Federal way Washington, My reason for teaching is to free students' minds and show them how deep the rabbit hole really goes. The way I teach them depends on the subject at the time and each students' prior experience that i can make a connection to, in other words, i flow like water, because if you put water in a cup it becomes the cup, if you put water in a bowl it becomes the bow, be like water my friend. | ||
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Lemonwalrus
United States5465 Posts
Do it. | ||
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starfries
Canada3508 Posts
On February 05 2011 05:36 Empyrean wrote: The last assertion is incorrect. 0^0 is an indeterminate form. yeah I know, but most people define it as 1 because of how nice it makes math edit: part of the mind-blowing comes from how hilariously complicated some of the arguments are for defining it that way it's one of the thermal exhaust ports in the death star of mathematics that we've nailed a bunch of planks over as a fairly effective but not really satisfying solution | ||
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