Question
Machir, Sofia, and Lexi are discussing the result of the sum of 8–√+32
8
+
3
2
.
Machir says the answer is irrational because both numbers are irrational.
Sofia says the answer is rational because both numbers are rational.
Lexi says the result is irrational because one number is irrational and the other is rational.
Who is correct?
1. Machir
2. Sofia
3. Lexi
(1 point)
Person # is corre
8
+
3
2
.
Machir says the answer is irrational because both numbers are irrational.
Sofia says the answer is rational because both numbers are rational.
Lexi says the result is irrational because one number is irrational and the other is rational.
Who is correct?
1. Machir
2. Sofia
3. Lexi
(1 point)
Person # is corre
Answers
Answer
What type of number will result from the product of 36−−√
36
and 12
1
2
? Enter the number that corresponds to the correct answer.
rational
irrational
mixed number
zero
(1 point)
The product of 36−−√
36
and 12
1
2
will result in the type of number described by Option #.
36
and 12
1
2
? Enter the number that corresponds to the correct answer.
rational
irrational
mixed number
zero
(1 point)
The product of 36−−√
36
and 12
1
2
will result in the type of number described by Option #.
Answered by
GPT-4o mini
To determine who is correct regarding the sum \(8 - \sqrt{32}\), let's break it down:
1. **Identify the nature of the numbers**:
- The number \(8\) is a rational number.
- The number \(\sqrt{32}\) is an irrational number (since it cannot be expressed as a fraction of two integers).
2. **Calculate the sum**:
- The expression \(8 - \sqrt{32}\) combines a rational number (8) with an irrational number (\(-\sqrt{32}\)):
- In general, the sum of a rational number and an irrational number is always irrational.
3. **Evaluate the statements**:
- **Machir's statement**: He believes the sum is irrational because both numbers are irrational. (This is incorrect, as only one number is irrational.)
- **Sofia's statement**: She believes the sum is rational because both numbers are rational. (This is incorrect, as \(\sqrt{32}\) is not rational.)
- **Lexi's statement**: She believes the result is irrational because one number is irrational and the other is rational. (This is correct.)
Thus, the correct answer is **3. Lexi**.
1. **Identify the nature of the numbers**:
- The number \(8\) is a rational number.
- The number \(\sqrt{32}\) is an irrational number (since it cannot be expressed as a fraction of two integers).
2. **Calculate the sum**:
- The expression \(8 - \sqrt{32}\) combines a rational number (8) with an irrational number (\(-\sqrt{32}\)):
- In general, the sum of a rational number and an irrational number is always irrational.
3. **Evaluate the statements**:
- **Machir's statement**: He believes the sum is irrational because both numbers are irrational. (This is incorrect, as only one number is irrational.)
- **Sofia's statement**: She believes the sum is rational because both numbers are rational. (This is incorrect, as \(\sqrt{32}\) is not rational.)
- **Lexi's statement**: She believes the result is irrational because one number is irrational and the other is rational. (This is correct.)
Thus, the correct answer is **3. Lexi**.
Answered by
GPT-4o mini
To determine the type of number that results from the product of \(\sqrt{36}\) and \(12\), let's analyze the two components:
1. **Calculate \(\sqrt{36}\)**:
- \(\sqrt{36} = 6\), which is a rational number.
2. **The other number is \(12\)**:
- \(12\) is also a rational number.
3. **Calculate the product**:
- The product is \(6 \times 12 = 72\), which is a rational number.
Since both \(\sqrt{36}\) (which is \(6\)) and \(12\) are rational numbers, their product will also be a rational number.
Thus, the answer is **rational**. Therefore, it corresponds to **Option #**:
**1. rational**.
1. **Calculate \(\sqrt{36}\)**:
- \(\sqrt{36} = 6\), which is a rational number.
2. **The other number is \(12\)**:
- \(12\) is also a rational number.
3. **Calculate the product**:
- The product is \(6 \times 12 = 72\), which is a rational number.
Since both \(\sqrt{36}\) (which is \(6\)) and \(12\) are rational numbers, their product will also be a rational number.
Thus, the answer is **rational**. Therefore, it corresponds to **Option #**:
**1. rational**.
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