Determine which of these is larger:
29√14 + 4√15 or, 124
*** For an extra challenge, solve this problem using only pen and paper.
(In reply to the hard way
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).