The number u is irrational. Which statement about sqrt 3 - u is true? Choices: (A)sqrt 3 - u is rational. (B)sqrt 3 - u is irrational. (C)sqrt 3 - u can be rational or irrational, depending on the value of u.

Question

The number u is irrational. Which statement about sqrt 3 - u is true?   Choices: (A)sqrt 3 - u is rational. (B)sqrt 3 - u is irrational. (C)sqrt 3 - u can be rational or irrational, depending on the value of u.

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Identify Type of Number: Identify whether sqrt(3) is a rational or irrational number. Since 3 is not a perfect square, the square root of 3 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. It depends on the specific numbers involved.Analyze Outcomes for sqrt(3) - u: Analyze the possible outcomes for sqrt(3) - u. If u is an irrational number that is not related to sqrt(3), then sqrt(3) - u is likely to be irrational. However, if u is some irrational number that, when subtracted from sqrt(3), results in a rational number (for example, if u = sqrt(3) + a rational number), then sqrt(3) - u could be rational.Determine Correct Choice: Determine the correct choice based on the analysis. Since there are scenarios where sqrt(3) - u could be rational and others where it could be irrational, the correct statement is that sqrt(3) - u can be rational or irrational, depending on the value of u.

The number $u$ is irrational. Which statement about $\sqrt{3} - u$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{3} - u$ is rational. $\newline$ (B) $\sqrt{3} - u$ is irrational. $\newline$ (C) $\sqrt{3} - u$ can be rational or irrational, depending on the value of $u$ .

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