To evaluate the expression \( 56 + \sqrt{91} \), we first need to calculate the square root of 91.
The square root of 91 is approximately:
\[ \sqrt{91} \approx 9.539392 \]
Now, we can add this value to 56:
\[ 56 + \sqrt{91} \approx 56 + 9.539392 \approx 65.539392 \]
This result \( 65.539392 \) is not one of the options provided.
Let's explore if there's any misunderstanding or whether the options relate to a different sum. However, if we were to assume the options came from just \( \sqrt{91} \) or \( 56 + \sqrt{91} \), the closest to an actual sum calculation would likely be pointing towards the irrational nature of \( \sqrt{91} \) since it cannot be expressed as a clean fraction.
Reviewing the options:
- 9.58297100… , irrational - Not a match for √91 or related to it.
- 10.3727253… , irrational - Not close to our calculations.
- 91.83¯¯¯ , rational - Related to another computation.
- 10.3¯¯¯ , rational - Also does not fit our findings.
To summarize, \(56 + \sqrt{91}\) results in \( \approx 65.539 \), and the result derived from \( \sqrt{91}\) is irrational, indicating any inclusion of that sum is possibly exploring the nature of irrational vs rational. However, clearer computations do not fit squarely here based on calculations.
For the sake of confirming:
We conclude that the sum \( 56 + \sqrt{91} \) overall can be considered an irrational number since \( \sqrt{91} \) itself is irrational, and the sum is not simplistic beyond this.
So no exact option matches computations, but it would affirm to categorize as irrational due to √91 contributing that aspect.