Question
According to the Closure Property, 15+615+6 would result in what type of number?(1 point) Responses Integer Integer Zero Zero Rational Rational Irrational Irrational Question 2 According to the Closure Property, which of these differences would result in a rational number?(1 point) Responses 5–√−2–√5−2square root of 5 minus square root of 2 36−−√−2336−23square root of 36 minus 2 thirds π−1π−1pi minus 1 6.2¯¯¯−3–√6.2¯−36 point repeating 2 minus square root of 3
Answers
GPT-4o mini
**Question 1:**
To apply the Closure Property, we look at the expression \( 15 + 615 + 6 \). Since all the numbers involved (15, 615, and 6) are integers, and the sum of integers is also an integer, the result of the operation will be an integer.
**Response:** Integer
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**Question 2:**
To determine which difference results in a rational number, let's analyze each option:
1. **\( 5 - \sqrt{2} - \sqrt{5} \)**:
- \(\sqrt{2}\) and \(\sqrt{5}\) are both irrational numbers. The difference of a rational number (5) and an irrational number (\(\sqrt{2} + \sqrt{5}\)) is irrational.
2. **\( \sqrt{36} - \frac{2}{3} \)**:
- \(\sqrt{36} = 6\), which is rational. So \(6 - \frac{2}{3}\) is also rational.
3. **\( \pi - 1 \)**:
- \(\pi\) is irrational and \(1\) is rational. The difference of an irrational and a rational number is irrational.
4. **\( 6.2\overline{2} - \sqrt{3} \)**:
- \(6.2\overline{2}\) is rational (it's a repeating decimal). The difference of a rational number and an irrational number (\(\sqrt{3}\)) will also be irrational.
**Response:** \( \sqrt{36} - \frac{2}{3} \)
To apply the Closure Property, we look at the expression \( 15 + 615 + 6 \). Since all the numbers involved (15, 615, and 6) are integers, and the sum of integers is also an integer, the result of the operation will be an integer.
**Response:** Integer
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**Question 2:**
To determine which difference results in a rational number, let's analyze each option:
1. **\( 5 - \sqrt{2} - \sqrt{5} \)**:
- \(\sqrt{2}\) and \(\sqrt{5}\) are both irrational numbers. The difference of a rational number (5) and an irrational number (\(\sqrt{2} + \sqrt{5}\)) is irrational.
2. **\( \sqrt{36} - \frac{2}{3} \)**:
- \(\sqrt{36} = 6\), which is rational. So \(6 - \frac{2}{3}\) is also rational.
3. **\( \pi - 1 \)**:
- \(\pi\) is irrational and \(1\) is rational. The difference of an irrational and a rational number is irrational.
4. **\( 6.2\overline{2} - \sqrt{3} \)**:
- \(6.2\overline{2}\) is rational (it's a repeating decimal). The difference of a rational number and an irrational number (\(\sqrt{3}\)) will also be irrational.
**Response:** \( \sqrt{36} - \frac{2}{3} \)