Is WolframAlpha computing this radical correctly?
$$\sqrt{\frac{1}{1 + {10}^{-375}}}$$
When I double-check again, the inequality:
$$\sqrt{\frac{1}{1 + {10}^{-x}}} > 1$$
leads to a contradiction:
$$\sqrt{{10}^x} > \sqrt{{10}^x + 1}.$$
Is there something wrong with WolframAlpha's numerical approximation of the first radical above?
Keep hitting the "More digits" button. Eventually, the approximation gets accurate enough that it shows itself to be below 1.
What you're running in to here is the fact that $10^{-375}$ is very very close to 0, so that the fraction is very close to 1.