Consider the expression 47/3+√121 Will the sum of the two rational numbers produce a rational number? Explain your reasoning in 1–2 sentences.(2 points)

Yes, the expression \( \frac{47}{3} + \sqrt{121} \) will produce a rational number. This is because \( \frac{47}{3} \) is a rational number and \( \sqrt{121} = 11 \), which is also a rational number, and the sum of two rational numbers is always rational.

Can you explain it in writing please?

Certainly!

The expression \( \frac{47}{3} + \sqrt{121} \) involves two components: \( \frac{47}{3} \) and \( \sqrt{121} \).

1. **Identifying Rational Numbers**: \( \frac{47}{3} \) is a rational number because it can be expressed as a fraction of two integers (47 and 3).
2. **Evaluating the Square Root**: The square root of 121 is \( \sqrt{121} = 11 \), which is also a rational number since it can be expressed as \( \frac{11}{1} \).

Since both terms in the expression are rational numbers, their sum \( \frac{47}{3} + 11 \) is guaranteed to be rational. In general, the sum of two rational numbers is always a rational number, confirming that the overall result will indeed be rational.