To find the sum of \( \frac{5}{6} + \sqrt{91} \), we first need to evaluate \( \sqrt{91} \).
Calculating \( \sqrt{91} \):
The square root of 91 is approximately \( 9.539 \) (since \( 9^2 = 81 \) and \( 10^2 = 100 \)).
Now, adding \( \frac{5}{6} \) to \( \sqrt{91} \):
Convert \( \frac{5}{6} \) to a decimal for easier addition:
\[ \frac{5}{6} \approx 0.8333 \]
Now we can add the two values together:
\[ \frac{5}{6} + \sqrt{91} \approx 0.8333 + 9.539 \approx 10.3723 \]
So the sum \( \frac{5}{6} + \sqrt{91} \) is approximately \( 10.3723 \).
Classification:
The expression \( \frac{5}{6} + \sqrt{91} \) consists of a rational number \( \frac{5}{6} \) and an irrational number \( \sqrt{91} \). The sum of a rational number and an irrational number is always irrational.
Thus, the sum \( \frac{5}{6} + \sqrt{91} \) is classified as an irrational number.