My Math Forum Computing Average of Surds.

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 April 19th, 2017, 12:48 AM #1 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Computing Average of Surds. Can we compute average of Surds? Example - 2√3,4√5,3√2,5√4,6√7,8√3,9√2 Thanks & Regards, Prashant S Akerkar
 April 19th, 2017, 12:51 AM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,597 Thanks: 546 Math Focus: Yet to find out. $Avg = \dfrac{2√3 + 4√5 + 3√2 + 5√4 + 6√7 + 8√3 + 9√2}{7}$
 April 19th, 2017, 04:15 AM #3 Senior Member   Joined: May 2016 From: USA Posts: 1,038 Thanks: 423 Surds are just numbers so of course we can calculate an average of them. Silly question.
 April 19th, 2017, 04:25 AM #4 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,364 Thanks: 100 It's not a silly question. It's about combining surds. You can add like surds but not unlike surds.
April 19th, 2017, 07:13 AM   #5
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 Originally Posted by zylo You can add like surds but not unlike surds.
That is plain wrong.

$\sqrt{7} + \sqrt{7} = 2\sqrt{7}.$

$\sqrt{2} + \sqrt{5} = \sqrt{2} + \sqrt{5}.$

Then that too is an exact answer.

If you object that the second is not exact because it cannot be expressed exactly in decimals, then express the first exactly in decimals.

Silly questions invite even sillier responses.

 April 19th, 2017, 09:41 AM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond prashantakerkar, I fear you are not being taken seriously. Do you have any idea why that might be? Thanks from JeffM1
 April 19th, 2017, 09:53 AM #7 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Thanks. How we can further simplify to get the average of seven numbers which are Surds? What's the answer for the above? Thanks & Regards, Prashant S Akerkar
April 19th, 2017, 09:59 AM   #8
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Quote:
 Originally Posted by prashantakerkar Thanks. How we can further simplify to get the average of seven numbers which are Surds? What's the answer for the above? Thanks & Regards, Prashant S Akerkar
Joppy already gave you the mathematically exact answer. If you want an approximate answer expressed in decimal notation, you must INDIVIDUALLY: approximate each surd to several more decimals than you care about, do the resulting arithmetic, and round the result to the number of decimal places you care about.

Do you understand that decimal notation cannot express exactly all real numbers?

Last edited by JeffM1; April 19th, 2017 at 10:02 AM.

April 19th, 2017, 10:19 AM   #9
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Quote:
 Originally Posted by JeffM1 Do you understand that decimal notation cannot express exactly all real numbers?
No.

April 19th, 2017, 11:09 AM   #10
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Quote:
 Originally Posted by prashantakerkar Can we compute average of Surds?
...not to be confused with average length of Turds?

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