Let's calculate the sum \( \frac{5}{6} + \sqrt{91} \).
First, we compute \( \sqrt{91} \):
- The value of \( \sqrt{91} \) is approximately \( 9.539 \) (as \( 9.5^2 = 90.25 \) and \( 9.6^2 = 92.16 \)).
- Therefore, \( \sqrt{91} \) is between \( 9.5 \) and \( 9.6 \).
Next, we calculate \( \frac{5}{6} \) in decimal form:
- \( \frac{5}{6} \) is approximately \( 0.8333... \), which is rational.
Now, let's add these two numbers together: \[ \frac{5}{6} + \sqrt{91} \approx 0.8333 + 9.539 \approx 10.3723... \]
This gives us a rough approximation of \( 10.3723... \).
Now let's classify the sum:
- Since \( \sqrt{91} \) is an irrational number (square roots of non-perfect squares are irrational), and the sum of a rational number and an irrational number is always irrational, the overall sum \( \frac{5}{6} + \sqrt{91} \) must also be irrational.
Thus, the closest matching choice would be: D. 10.3727253 . . ., irrational.