perplexus.info :: Just Math : Root sum or integer?

Root sum or integer? (Posted on 2013-08-18)

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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re(2): the hard way....slightly softened

| Comment 3 of 6 |

14.5 is bigger than sqrt(210), as Ady seems to know. There are many ways that this can be proven. Here is one:

sqrt(14*15) =

sqrt((14.5 - .5)(14.5+.5)) =

sqrt((14.5)^2 - (.5)^2)) < 14.5

Posted by Steve Herman on 2013-08-18 18:47:27

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