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cannot be added together unless you resolve the number under the square root sign to a number that is not under the square root sign.
since

is equal to 1.732050808, then you replace

with 1.732050808 and you get 6 + 3*1.732050808 = 6 + 5.196152423 = 11.196152423.
if you do not resolve

to a number, then it has to be shown as you are showing it.

cannot be combined unless you resolve the number under the square root sign to a number that is not under the square root sign.
radicals have certain properties that allow some operations to be applied to them and do not allow other operations to be applied to them.
some of the properties are:

you can add square roots together if the term under the square root sign is the same.
example:

cannot be added together because the expressions under the square root sign are not the same.
sometimes you can, however, convert the terms under the square root sign so that they are the same.

is the same as

is the same as

is therefore equivalent to:

.
because the terms under the square root sign are the same, they can be combined to get:

.