To determine the best whole number square root that \( M \) represents, we first need to understand the values of \( R \) and \( S \) given that \( R = 8 \) and \( S = 8.5 \).
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Find the midpoint (or representation of M) between \( R \) and \( S \): \[ M = \frac{R + S}{2} = \frac{8 + 8.5}{2} = \frac{16.5}{2} = 8.25 \]
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Now, to find the square root of \( M \): We want to find \( \sqrt{M} = \sqrt{8.25} \).
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Estimate \( \sqrt{8.25} \): We know that:
- \( \sqrt{8} \approx 2.83 \)
- \( \sqrt{9} = 3 \)
Since \( 8.25 \) is between \( 8 \) and \( 9 \), we can conclude: \[ \sqrt{8} < \sqrt{8.25} < \sqrt{9} \] This implies: \[ 2.83 < \sqrt{8.25} < 3 \]
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Determining the best whole number: The best whole number for \( \sqrt{M} \) would be \( 3 \), since \( \sqrt{8.25} \) is closer to \( 3 \) than it is to \( 2 \).
Thus, the best whole number square root that \( M \) represents is approximately:
\[ \boxed{3} \]
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