What is #sqrt(10) + sqrt(10)# ?

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Answer 1 · 2016-05-01T11:45:26

#sqrt(10)+sqrt(10) = 2sqrt(10) = sqrt(40)#

A little slower:

#sqrt(10)+sqrt(10) = 1sqrt(10) +1sqrt(10) = (1+1) sqrt(10) = 2 sqrt(10)#

#= sqrt(2^2)sqrt(10) = sqrt(4)sqrt(10) = sqrt(4*10) = sqrt(40)#

I'm not sure what else to say about this except that:

#sqrt(10) + sqrt(10) != sqrt(20)#

#sqrt# is a non-linear operation, so in general:

#sqrt(a) + sqrt(b) != sqrt(a+b)#

(There are exceptions, e.g. #sqrt(a) + sqrt(0) = sqrt(a+0)#)