Question

Machir, Sofia, and Lexi are discussing the result of the sum of 8–√+32
.

Machir says the answer is irrational because both numbers are irrational.

Sofia says the answer is rational because both numbers are rational.

Lexi says the result is irrational because one number is irrational and the other is rational.

Who is correct?

1. Machir

2. Sofia

3. Lexi

Answer 1

Let's break down the expression \(8 - \sqrt{+32}\).

First, we can simplify \(\sqrt{32}\):

\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}
\]

Now, substituting this back into the expression gives us:

\[
8 - \sqrt{32} = 8 - 4\sqrt{2}
\]

Next, we need to evaluate the rationality of the result \(8 - 4\sqrt{2}\).

- The number \(8\) is a rational number.
- The number \(4\sqrt{2}\) is irrational (since \(\sqrt{2}\) is irrational).

Now, when a rational number (like \(8\)) is subtracted from an irrational number (like \(4\sqrt{2}\)), the result is still irrational.

To summarize:

1. Machir's argument is incorrect because he states both numbers are irrational.
2. Sofia is incorrect because she claims both numbers are rational.
3. Lexi is correct because she correctly notes that one number is irrational and the other is rational, leading to an overall irrational result.

Thus, **Lexi** is correct. The answer is \( \boxed{3} \).