To find the best representation of \( \sqrt{13} \) on a number line, we first need to estimate its approximate value.
Calculating \( \sqrt{13} \):
- We know that \( 3^2 = 9 \) and \( 4^2 = 16 \), so \( \sqrt{13} \) is between 3 and 4.
- To get a more precise estimate, we can try squaring numbers between 3 and 4.
Calculating:
- \( 3.5^2 = 12.25 \) (too low)
- \( 3.6^2 = 12.96 \) (still too low)
- \( 3.7^2 = 13.69 \) (a bit too high)
This suggests that \( \sqrt{13} \) is approximately 3.6 or 3.7.
Thus, on a number line, \( \sqrt{13} \) would be represented as a point near 3.6, which is between 3 and 4.
You should check the options (A, B, C, D) to see which one is closest to 3.6.
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