To find the best representation of \( \sqrt{13} \) on the number line, we first approximate its value.
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Calculate \( \sqrt{13} \):
- Since \( 3^2 = 9 \) and \( 4^2 = 16 \), it's clear that \( 3 < \sqrt{13} < 4 \).
- A more precise estimate can be found by calculating \( 3.6^2 \) and \( 3.7^2 \):
- \( 3.6^2 = 12.96 \) (which is less than 13)
- \( 3.7^2 = 13.69 \) (which is greater than 13)
- Therefore, \( 3.6 < \sqrt{13} < 3.7 \).
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Conclusion: Since \( \sqrt{13} \) is approximately \( 3.6 \), it would be best represented by a point on the number line that corresponds to this value.
Without the specific options labeled A, B, C, and D shown, you should choose the point that is closest to \( 3.6 \) on your given number line.
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