how would the following be simplified: root 6 divided by 2 + root 2 divided by 2?

Answer 1

Answers bother me on this one, for they all seem more complex than the original expression. (Some of the answers above are wrong, by the way).
My solution is as follows:
Knowing that sqrt6 = sqrt3 x sqrt2, then
(sqrt6)/2 + (sqrt2)/2 = (sqrt 3 x sqrt2)/2 + (sqrt2)/2
= 1/2{sqrt2(sqrt3 + 1}
This cannot be made simpler, and looks far more cumbersome than the original!!
I think a valid answer would be that the expression cannot be simplified- but you'd have to show working, nevertheless.

Answer 2

(sqrt6 / 2) + (sqrt2 / 2) = (sqrt6 + sqrt2)/2
sqrt6=sqrt3*sqrt2
therefore (sqrt6 + sqrt2)/2 = (sqrt3*sqrt2 + sqrt2)/2 = (sqrt3 +1)*sqrt2 / 2.

That could be the final answer. Or you could use sqrt2 / 2= 1/sqrt2
Therefore the final answer is (sqrt3+1)/sqrt2.

However this may not be the desired answer, as normally you don't want sqrts on the bottom of fractions.

Answer 3

(√6 / 2) / [ (2 + √2) / 2 ]
= √ 6 / (2 + √2)
= √6.(2 - √2) / 2

Answer 4

root6/2 + root2/root2 = root3*root2/root2*root2 + 1
= root3/root2 + 1
=1.73/1.41 + 1
= 1.23 + 1
= 2.23