Question

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)

Answer 1

47/3+11

Answer 2

To evaluate the expression \( \frac{47}{3} + \sqrt{121} \), we first simplify \( \sqrt{121} = 11 \), which is a rational number. The sum of two rational numbers, \( \frac{47}{3} \) (which is rational) and \( 11 \) (also rational), will produce a rational number. Therefore, the overall expression will yield a rational result.

Answer 3

To evaluate the expression \( \frac{47}{3} + 11 \), we can express \( 11 \) as a fraction to combine the two terms:

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

Now we can add the two fractions:

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

Thus, \( \frac{47}{3} + 11 = \frac{80}{3} \). This is a rational number.