To find the approximate value of \( \sqrt{103} \), we can first determine perfect squares close to 103:
- \( 10^2 = 100 \)
- \( 11^2 = 121 \)
Since \( 100 < 103 < 121 \), we know that \( \sqrt{103} \) is between 10 and 11.
To refine our estimate, we can try some values between 10 and 11:
- \( 10.1^2 = 102.01 \) (which is slightly less than 103)
- \( 10.2^2 = 104.04 \) (which is slightly more than 103)
So we can conclude that \( \sqrt{103} \) is between 10.1 and 10.2.
For a more precise calculation, using a calculator, we find:
\[ \sqrt{103} \approx 10.148 \]
Rounding to the nearest tenth, \( \sqrt{103} \approx 10.1 \).
So, the approximate number value of \( \sqrt{103} \) is:
10.1