Which number produces an irrational number when added to 0.5?

Question

Group of answer choices

/````7 (pretend that the 7 is underneath the line thats what im trying to do but i dont have the symbol)

/````16 (same for this number)

0.555...

1/3

Answer 1

To determine which number produces an irrational number when added to 0.5, let's analyze each choice:

1. /````7 (This represents \(\sqrt{7}\)):

   • \(0.5 + \sqrt{7}\) is irrational since adding a rational number (0.5) to an irrational number (\(\sqrt{7}\)) results in an irrational number.

2. /````16 (This represents \(\sqrt{16}\)):

   • \(\sqrt{16} = 4\), which is rational. Therefore, \(0.5 + 4 = 4.5\) is also rational.

3. 0.555...:

   • This is a repeating decimal, which is rational. Thus, \(0.5 + 0.555... = 1.055...\), which is also rational.

4. 1/3:

   • This is a rational number. Therefore, \(0.5 + \frac{1}{3}\) is also rational (specifically, it would equal \(0.833...\)).

In conclusion, the only number from the choices that, when added to 0.5, produces an irrational number is:

/````7 (or \(\sqrt{7}\)).

Answer 2

so sorry the first one was supposed to be /`````3 not 7. which one is right now?

Answer 3

No problem! Let’s evaluate the new first choice, \(\sqrt{3}\), along with the other options:

1. /````3 (This represents \(\sqrt{3}\)):

   • \(0.5 + \sqrt{3}\) is irrational since adding a rational number (0.5) to an irrational number (\(\sqrt{3}\)) results in an irrational number.

2. /````16 (This represents \(\sqrt{16}\)):

   • \(\sqrt{16} = 4\), which is rational. Thus, \(0.5 + 4 = 4.5\) is also rational.

3. 0.555...:

   • This is a repeating decimal, which is rational. Therefore, \(0.5 + 0.555... = 1.055...\), which is also rational.

4. 1/3:

   • This is a rational number. Therefore, \(0.5 + \frac{1}{3}\) is also rational (specifically, it would equal \(0.833...\)).

Since \(\sqrt{3}\) is an irrational number, the only choice that produces an irrational number when added to 0.5 is:

/````3 (or \(\sqrt{3}\)).