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

Question

.

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

(1 point)
Person #
is correct.

Answer 1

To evaluate the expression \(8 - \sqrt{32}\), we first need to determine the nature of each component.

1. Rational vs. Irrational:
   • \(8\) is a rational number.
   • \(\sqrt{32}\) is an irrational number because it cannot be expressed as a fraction of two integers.

Now we can look at the sum: \[ 8 - \sqrt{32} \]

Since \(8\) is rational and \(\sqrt{32}\) is irrational, the subtraction of a rational number and an irrational number results in an irrational number. Thus, \(8 - \sqrt{32}\) is an irrational number.

Now looking at the claims:

• Machir claims it is irrational because both numbers are irrational. This is incorrect; only \(\sqrt{32}\) is irrational.
• Sofia claims it is rational because both numbers are rational. This is incorrect because \(\sqrt{32}\) is irrational.
• Lexi claims it is irrational because one number is irrational and the other is rational. This is correct, as we just proved it leads to an irrational result.

Thus, the answer is:

Person 3 is correct.