Question
Find the sum and then classify it.56+91−−√ (1 point)Responses10.3¯¯¯, rational10 point repeating 3, rational9.58297100…, irrational9 point 5 8 2 9 7 1 0 0 dots, irrational91.83¯¯¯, rational91 point 8 repeating 3, rational10.3727253…, irrational10 point 3 7 2 7 2 5 3 dots, irrational
Answers
GPT-4o mini
To find the sum \( 56 + \sqrt{91} \), we first need to calculate \( \sqrt{91} \).
The approximate value of \( \sqrt{91} \) is about 9.539. Therefore:
\[
56 + \sqrt{91} \approx 56 + 9.539 \approx 65.539
\]
Now, we need to classify the sum \( 56 + \sqrt{91} \).
**Classification:**
- The number 56 is a rational number (it can be expressed as a fraction, \( \frac{56}{1} \)).
- The square root of any non-perfect square, like 91, is an irrational number. Thus, \( \sqrt{91} \) is irrational.
The sum of a rational number and an irrational number is always irrational. Therefore, \( 56 + \sqrt{91} \) is classified as irrational.
**Final answer:**
\( 56 + \sqrt{91} \) is approximately \( 65.539 \) and is an **irrational number**.
The approximate value of \( \sqrt{91} \) is about 9.539. Therefore:
\[
56 + \sqrt{91} \approx 56 + 9.539 \approx 65.539
\]
Now, we need to classify the sum \( 56 + \sqrt{91} \).
**Classification:**
- The number 56 is a rational number (it can be expressed as a fraction, \( \frac{56}{1} \)).
- The square root of any non-perfect square, like 91, is an irrational number. Thus, \( \sqrt{91} \) is irrational.
The sum of a rational number and an irrational number is always irrational. Therefore, \( 56 + \sqrt{91} \) is classified as irrational.
**Final answer:**
\( 56 + \sqrt{91} \) is approximately \( 65.539 \) and is an **irrational number**.