Consider the expression 47/3+121exponent1/2

To evaluate the expression \( \frac{47}{3} + 121^{1/2} \), we first look at each part. The term \( \frac{47}{3} \) is a rational number since it is a fraction of two integers. The term \( 121^{1/2} \) simplifies to \( 11 \) (since \( 11^2 = 121 \)), which is also a rational number.

When we add two rational numbers together, the result is always a rational number. Therefore, the sum \( \frac{47}{3} + 11 \) is rational. To compute this sum, we convert \( 11 \) into a fraction with a common denominator:

\[
11 = \frac{33}{3}
\]

Now we can add:

\[
\frac{47}{3} + \frac{33}{3} = \frac{47 + 33}{3} = \frac{80}{3}
\]

Thus, the sum is \( \frac{80}{3} \), which is rational.