According to the Closure Property, which of these sums would result in a rational number?(1 point)

Question

Responses

12−−√+14
12
+
1
4
square root of 12 plus 1 fourth

5–√+7.89
5
+
7.89
square root of 5 plus 7 point 8 9

8.5¯¯¯+π
8.
5
¯
+
π
8 point repeating 5 plus pi

49−−√+2.33

Answer 1

To determine which of the sums from the given options results in a rational number, we need to analyze each expression based on the properties of rational and irrational numbers.

1. \(\sqrt{12} + \frac{1}{4}\):

   • \(\sqrt{12}\) is irrational (approximately \(3.464\)).
   • Since the sum of a rational number (like \(\frac{1}{4}\)) and an irrational number is irrational, this sum is irrational.

2. \(\sqrt{5} + 7.89\):

   • \(\sqrt{5}\) is irrational (approximately \(2.236\)).
   • The number \(7.89\) is rational.
   • The sum of an irrational number and a rational number is also irrational, so this sum is irrational.

3. \(8.5 + \pi\):

   • \(8.5\) is rational.
   • \(\pi\) is irrational (approximately \(3.14159\)).
   • The sum of a rational number and an irrational number is irrational, so this sum is irrational.

4. \(\sqrt{49} + 2.33\):

   • \(\sqrt{49} = 7\), which is a rational number.
   • \(2.33\) is also a rational number.
   • The sum of two rational numbers is rational, so this sum is rational.

Based on this analysis, the sum that results in a rational number is:

\(\sqrt{49} + 2.33\)