To find the sum \( 56 + \sqrt{91} \), we first need to calculate \( \sqrt{91} \).
The decimal approximation of \( \sqrt{91} \) is approximately \( 9.539 \).
Now we can calculate the sum:
\[ 56 + \sqrt{91} \approx 56 + 9.539 \approx 65.539 \]
Now we will classify the result.
- The number \( 56 \) is a rational number.
- The number \( \sqrt{91} \) is an irrational number (since \( 91 \) is not a perfect square).
- The sum of a rational number and an irrational number is irrational.
Thus, the sum \( 56 + \sqrt{91} \) is an irrational number.
Based on this analysis, the closest response that matches our calculation and classification is:
10.3727253…, irrational (since \( 10.3727253... \) is a possible representation of \( \sqrt{91} \) added to the integer 56).
However, none of the provided options directly reflect the calculated sum. Therefore, it's confirmed that the sum results in \( 65.539... \), which is irrational, but the presented options seem not to match correctly with the actual calculation.