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Root sum or integer? (Posted on 2013-08-18) Difficulty: 3 of 5
Determine which of these is larger:
       29√14 + 4√15  or,    124
*** For an extra challenge, solve this problem using only pen and paper.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re(2): the hard way....slightly softened | Comment 4 of 6 |
(In reply to re: the hard way....slightly softened by Ady TZIDON)

It is not "as Ady seems to know"- 

 I've mentioned in the text:
-easy to check that 14.5^2=210.25 

To square any number ending by 5, say 10n+5 you mentaly
multiply n by n+1 and append the result by 25,
e.g. to evaluate 145^2 ==>  14*15=210,
 so the result is   21025.  In our case  210.25 .

Since you like proofs to a rule of thumb:

(10n+5)^2=100n^2+100n+25 =100n*(n+1)+25

Few examples: (no pen & paper)
65==>4225,     115==>13225,     1005==>1010025. 


  Posted by Ady TZIDON on 2013-08-19 00:44:40
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