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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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Solution re: the hard way....slightly softened | Comment 2 of 6 |
(In reply to the hard way by Daniel)

After squaring and subtracting 12014 from both sides

the problem boils down to comparing
12014+232*sqrt(210) and 15376
 
since 210 is midway between 196 and 225

14.5 is a pretty good approximation to sqrt(210)
-easy to check that 14.5^2=210.25 

The rest follows easily,
the left side is smaller than the right side, even when using  a slightly bigger value for sqrt(210).

  Posted by Ady TZIDON on 2013-08-18 15:37:14
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