To determine where \( \sqrt{58} \) falls on a number line, we start by calculating \( \sqrt{58} \).
Since \( 7^2 = 49 \) and \( 8^2 = 64 \), we know that:
\[ 7 < \sqrt{58} < 8 \]
Next, we can refine our estimate by finding the decimal value of \( \sqrt{58} \):
Using a calculator, we find:
\[ \sqrt{58} \approx 7.615773 \]
Next, we round \( 7.615773 \) to the nearest half. The halfway points are 7.5 and 8. Therefore, we round it as follows:
- Since \( 7.615773 \) is closer to \( 7.5 \) than \( 8 \), we round it to \( 7.5 \).
Thus, the number \( \sqrt{58} \) lies between:
- Whole number: 7 (the integer part)
- Rational number to the nearest half: 7.5
So, the correct choice from your responses is:
between 7.5 and 8.
1 answer