The number a is irrational. Which statement about a - sqrt 12 is true? Choices: (A)a - sqrt 12 is rational. (B)a - sqrt 12 is irrational. (C)a - sqrt 12 can be rational or irrational, depending on the value of a.

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The number a is irrational. Which statement about a - sqrt 12 is true?   Choices: (A)a - sqrt 12 is rational. (B)a - sqrt 12 is irrational. (C)a - sqrt 12 can be rational or irrational, depending on the value of a.

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Identify Type of Number: Identify whether sqrt(12) is a rational or irrational number. 12 is not a perfect square, so its square root cannot be expressed as a simple fraction. sqrt(12) is an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational. For example, if a = sqrt(12), then a - sqrt(12) = sqrt(12) - sqrt(12) = 0, which is rational. However, if a is any irrational number not related to sqrt(12), then a - sqrt(12) is likely to be irrational.Determine Correct Statement: Determine the correct statement based on the properties of irrational numbers. Since we can find at least one case where a - sqrt(12) is rational (when a = sqrt(12)), and we know that in general, the difference between two unrelated irrational numbers is irrational, the correct statement is that a - sqrt(12) can be rational or irrational, depending on the value of a.

The number $a$ is irrational. Which statement about $a - \sqrt{12}$ is true? $\newline$ Choices: $\newline$ (A) $a - \sqrt{12}$ is rational. $\newline$ (B) $a - \sqrt{12}$ is irrational. $\newline$ (C) $a - \sqrt{12}$ can be rational or irrational, depending on the value of $a$ .

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