To find where \( \sqrt{58} \) falls on a number line, we first need to estimate this square root.
Calculating \( \sqrt{58} \):
- We know that \( 7^2 = 49 \) and \( 8^2 = 64 \). Therefore, \( \sqrt{58} \) is between 7 and 8.
Next, let's narrow it down more precisely to determine whether it's closer to 7.5 or to 8.
Calculating \( 7.5^2 \): \[ 7.5^2 = 56.25 \] Calculating \( 8^2 \): \[ 8^2 = 64 \]
Since \( 56.25 < 58 < 64 \), we can confirm that: \[ 7.5 < \sqrt{58} < 8 \]
To further estimate \( \sqrt{58} \), let's use a calculator or approximate method: \[ \sqrt{58} \approx 7.615 \]
Since \( 7.615 \) is closer to 7.5 than 8, we can conclude that \( \sqrt{58} \) is:
- Between 7.5 and 8.
Thus, the correct answer is between 7.5 and 8.
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