To simplify \(\sqrt{31000}\):
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First, we can break down \(31000\) into its prime factors. The number \(31000\) can be expressed as:
\[ 31000 = 31 \times 1000 = 31 \times 10^3 = 31 \times (10^2 \times 10) = 31 \times 100 \times 10 \]
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Then, we can further simplify it as \(31000 = 31 \times 100 \times 10 = 31 \times 10^3\).
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Taking the square root, we get:
\[ \sqrt{31000} = \sqrt{31 \times 1000} = \sqrt{31} \times \sqrt{1000} \]
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Since \(1000 = 10^3 = 10^2 \times 10 = 100 \times 10\), we can simplify:
\[ \sqrt{1000} = \sqrt{10^3} = 10^{3/2} = 10 \sqrt{10} \]
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Putting it all together, we get:
\[ \sqrt{31000} = \sqrt{31} \times 10 \sqrt{10} = 10 \sqrt{310} \]
Thus, we can't simplify it to a whole number but the nearest whole number approximation of \( \sqrt{31000} \) is \( 176\) (as \( 176^2 \) is close to \(31000\)).
However, from the given options (11, 2, 10), the most fitting response would be:
10 (since \(\sqrt{31000} \approx 176\) and we needed to give a simple response).