Observe that

Now,

so that


To decide which is the correct value, we need to examine the sign of
. It evaluates to 0 if

We have

Also,

and
increases as
increases, which means

Therefore for all
,

For example, when
, we get

Then the target expression has a negative sign at the given value of
:

Alternatively, we can try simplifying
by denesting the radical. Let
be non-zero integers (
) such that

Note that the left side must be positive.
Taking squares on both sides gives

Let
and
. Then



Only the first case leads to integer coefficients. Since
, one of
or
must be negative. We have

Now if
, then
, and

However,
, so
is negative, so we don't want this.
Instead, if
, then
, and thus

Then our target expression evaluates to
