Question
Find the sum and then classify it. 56+91−−√ (1 point) Responses 10.3¯¯¯ , rational 10 point repeating 3, rational 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
Answers
GPT-4o mini
To find the sum \( 56 + \sqrt{91} \):
1. First, we calculate the approximate value of \( \sqrt{91} \).
\[
\sqrt{91} \approx 9.539
\]
(The exact value can be calculated, but we will work with the approximate value for classification.)
2. Next, we add this to 56:
\[
56 + 9.539 \approx 65.539
\]
Now, let's classify the result.
- **Rational numbers** are numbers that can be expressed as the quotient of two integers (like fractions), while **irrational numbers** cannot be expressed this way and have non-repeating, non-terminating decimal expansions.
- Since \( \sqrt{91} \) is not a perfect square, it is an **irrational number**. The sum of a rational number (56) and an irrational number (\(\sqrt{91}\)) is always an **irrational number**.
Therefore, the sum \( 56 + \sqrt{91} \approx 65.539 \) is:
- **Irrational**.
Thus, the answer would be classified as \( 65.539 \), irrational. However, among the options you listed, we don't see this exact result, but we can confirm the concept that adding a rational number and an irrational number indeed results in an irrational number.
From your provided responses, the most relevant categorizations are likely:
- **9.58297100… , irrational**
or
- **10.3727253… , irrational**
Though these values don't match our precise calculation, they are classified correctly based on the mentioned principles of rationality and irrationality. Please select the option that you believe is most appropriate based on the context provided.
1. First, we calculate the approximate value of \( \sqrt{91} \).
\[
\sqrt{91} \approx 9.539
\]
(The exact value can be calculated, but we will work with the approximate value for classification.)
2. Next, we add this to 56:
\[
56 + 9.539 \approx 65.539
\]
Now, let's classify the result.
- **Rational numbers** are numbers that can be expressed as the quotient of two integers (like fractions), while **irrational numbers** cannot be expressed this way and have non-repeating, non-terminating decimal expansions.
- Since \( \sqrt{91} \) is not a perfect square, it is an **irrational number**. The sum of a rational number (56) and an irrational number (\(\sqrt{91}\)) is always an **irrational number**.
Therefore, the sum \( 56 + \sqrt{91} \approx 65.539 \) is:
- **Irrational**.
Thus, the answer would be classified as \( 65.539 \), irrational. However, among the options you listed, we don't see this exact result, but we can confirm the concept that adding a rational number and an irrational number indeed results in an irrational number.
From your provided responses, the most relevant categorizations are likely:
- **9.58297100… , irrational**
or
- **10.3727253… , irrational**
Though these values don't match our precise calculation, they are classified correctly based on the mentioned principles of rationality and irrationality. Please select the option that you believe is most appropriate based on the context provided.