To rewrite 812 (which is 8 raised to the 12th power) using a root, you can express it as:
\[ 8^{12} = (8^2)^6 = 64^6 \]
However, if you are specifically looking for a root representation that is simpler regarding \(8\) and \(12\), you could go with:
\[ 8^{12} = (8^{1/2})^{24} = \sqrt{8^{24}} \]
But since none of the responses given in your question directly show this clear representation for \(8^{12}\), let's find the most appropriate option using roots while still trying to maintain accuracy.
The response "8−√" seems to suggest a misunderstanding or lack of completeness.
The closest to correctly representing something akin to \(8^{12}\) in your responses technically is ambiguous given the notations used.
For proper mathematical expression, a better approach would be:
\[ 812 = (8^{12}) = \sqrt[12]{8^{144}} \]
You would want to ensure that "200" written as "root index 12" aligns correctly in evaluations.
If you could clarify the options further or any specifics of what you're looking to achieve by "using a root", that would help me provide targeted guidance.