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

Answer 1

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: \( \sqrt{36} - \frac{2}{3} \)