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. $sqrt(a) + sqrt(0) = sqrt(a+0)$ )

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