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 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).**