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I entered 3*sqrt3*sqrt3 and got an answer of 9.00000000001
does the real Prime make this same funny answer?
(04-23-2016 02:24 AM)SalivationArmy Wrote: [ -> ]I entered 3*sqrt3*sqrt3 and got an answer of 9.00000000001
does the real Prime make this same funny answer?
This funny answer is find in Home by me. In CAS, it make the correct answer: 9.
Remember the Home mode give an approximated result, while CAS don't. The definition of Home mode can be an explanation to this funny result.
I understand now.

Instead of logically multiplying 3 x 3 and placing the result under the sqrt like a human brain would, it's calculating the result of each of the sqrt3 to 10 or so digits the rounding off, which is NOT a perfect result, then working the problem.

human:
3* sqrt3 *sqrt3 =
3 * sqrt9 =
3 * 3 =
9

Honest calculator:
3* sqrt3 *sqrt3 =
3 * 1.73205080757 * 1.73205080757 =
9.00000000001
(The bolded digits are rounded off)

Nasa calculated the square root of three out to 10 million digits, you can imagine it a mess of a number. Here's the first 500 digits:

1.732050807568877293527446341505872366942805253810380628055806979451933016908800​0370811461867572485756
75626141415406703029969945094998952478811655512094373648528093231902305582067974​82010108467492326501
53123432669033228866506722546689218379712270471316603678615880190499865373798593​89467650347506576050
75661834812960610094760218719032508314582952395983299778982450828871446383291734​72241639845878553976
67958063818353666110843173780894378316102088305524901670023520711144288695990956​36579708716849807289
(04-23-2016 02:24 AM)SalivationArmy Wrote: [ -> ]I entered 3*sqrt3*sqrt3 and got an answer of 9.00000000001
does the real Prime make this same funny answer?

This answer is not funny, it's simply correct.

Like any other finite-precision calculator the Prime does not return sqrt 3. It returns a value that matches sqrt 3 in its first twelve digits, i.e. 1,73205080757.
But that's not sqrt 3 = 1,7320508075688772935274463415... etc. etc.

Now the Prime gives the exact answer based on this approximation of sqrt 3:

3 x 1,73205080757 = 5,19615242271
5,19615242271 x 1,73205080757 = 9,0000000000116675...

Which, rounded to 12 digits, is the result you see (9,00000000001).

Try sqrt 7 x sqrt 7 or sqrt 8 x sqrt 8. If your calculator works correctly you should not get 7 and 8 but 6,99999999998 and 8,00000000002.

Dieter
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