Let's simplify and evaluate the given expression, step by step, along with the provided options, and compare them numerically.
The expression given in the question is:
[tex]\[ -231 \sqrt{10} \][/tex]
We need to check which of the options correspond to this expression.
Option A:
[tex]\[ -77 \sqrt{30} \][/tex]
Evaluating this expression numerically:
[tex]\[ -77 \times \sqrt{30} \approx -77 \times 5.477 \approx -421.75 \][/tex]
Option B:
[tex]\[ -462 \sqrt{5} \][/tex]
Evaluating this expression numerically:
[tex]\[ -462 \times \sqrt{5} \approx -462 \times 2.236 \approx -1033.06 \][/tex]
Option C:
[tex]\[ -\sqrt{2310} \][/tex]
Evaluating this expression numerically:
[tex]\[ -\sqrt{2310} \approx -48.07 \][/tex]
Option D:
[tex]\[ -231 \sqrt{10} \][/tex]
Evaluating this expression numerically:
[tex]\[ -231 \times \sqrt{10} \approx -231 \times 3.162 \approx -730.49 \][/tex]
Comparing all the evaluated options with the given expression:
- Option A: [tex]\[ -421.75 \][/tex]
- Option B: [tex]\[ -1033.06 \][/tex]
- Option C: [tex]\[ -48.07 \][/tex]
- Option D: [tex]\[ -730.49 \][/tex]
The correct answer is Option D, because it exactly matches the expression [tex]\(-231 \sqrt{10}\)[/tex].
Therefore, the correct selection is:
[tex]\[ \boxed{-231 \sqrt{10}} \][/tex]
