Question

Find the sum and then classify it.

56+91−−√
(1 point)
Responses

91.83¯¯¯
, rational
91 point 8 repeating 3, rational

9.58297100…
, irrational
9 point 5 8 2 9 7 1 0 0 dots, irrational

10.3727253…
, irrational
10 point 3 7 2 7 2 5 3 dots, irrational

10.3¯¯¯
, rational

Answer 1

To find the sum of \( 56 + \sqrt{91} \), we first need to calculate the value of \( \sqrt{91} \).

Using a calculator or performing the calculation, we have:

\[
\sqrt{91} \approx 9.539392
\]

Now, we'll compute the total:

\[
56 + \sqrt{91} \approx 56 + 9.539392 \approx 65.539392
\]

Next, we need to classify the result. The sum \( 65.539392 \) is approximately 65.54, which is a terminating decimal, and thus it is rational.

Since the square root of \( 91 \) is an irrational number, \( 56 + \sqrt{91} \) (which is a sum of a rational number and an irrational number) will also be irrational. Therefore, instead of the approximate decimal, we focus on the classification.

Looking through the possible responses, here is the classification:
- The sum \( 56 + \sqrt{91} \) is irrational.

So, the correct response among the options is:

9.58297100…, irrational
This is the closest option, though please note that the original sum calculates closer to \( 65.54 \) when rounded, not \( 9.58297... \).

The best response to provide clarity to your request is:

65.54..., irrational.