According to the Closure Property, 14+2–√14+2 would result in what type of number?(1 point) Responses Integer Integer Zero Zero Rational Rational Irrational Irrational Check Answer Question 2 According to the Closure Property, which of these differences would result in a rational number?(1 point) Responses 64−−√−7–√64−7square root of 64 minus square root of 7 49−−√−1449−14square root of 49 minus 1 fourth 5–√−3.25−3.2square root of 5 minus 3 point 2 6.2¯¯¯−π6.2¯−π6 point repeating 2 minus pi

Answer 1

Let's go through the questions one by one.

Question 1

You are asked to determine the type of number resulting from the expression \( 14 + 2 - \sqrt{14 + 2} \).

1. Calculate \( 14 + 2 \): \[ 14 + 2 = 16 \]

2. Calculate \( \sqrt{16} \): \[ \sqrt{16} = 4 \]

3. Now substitute back into the expression: \[ 16 - 4 = 12 \]

Now, we identify the type of number:

• \( 12 \) is an integer and also a rational number (since all integers are rational numbers).

Based solely on the options, the most straightforward answer would be Integer.

Question 2

You need to identify which of the given differences results in a rational number:

1. Option 1: \( \sqrt{64} - \sqrt{7} \)

   • \( \sqrt{64} = 8 \), so \( 8 - \sqrt{7} \). Since \( \sqrt{7} \) is irrational, this result is also irrational.

2. Option 2: \( \sqrt{49} - \frac{1}{4} \)

   • \( \sqrt{49} = 7 \), so \( 7 - \frac{1}{4} = \frac{28}{4} - \frac{1}{4} = \frac{27}{4} \), which is rational.

3. Option 3: \( \sqrt{5} - 3.2 \)

   • \( \sqrt{5} \) is irrational, and subtracting a rational number (3.2) from an irrational number results in an irrational number.

4. Option 4: \( 6.2 - \pi \)

   • \( 6.2 \) is rational, while \( \pi \) is irrational. Thus, their difference is also irrational.

Based on the evaluation, the only option that results in a rational number is Option 2: \( \sqrt{49} - \frac{1}{4} \).

Summary

• Question 1 Answer: Integer
• Question 2 Answer: \( \sqrt{49} - \frac{1}{4} \) (which simplifies to a rational number).