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

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Q. The number tt is irrational. Which statement about 3t\sqrt{3} - t is true?\newlineChoices:\newline(A) 3t\sqrt{3} - t is rational.\newline(B) 3t\sqrt{3} - t is irrational.\newline(C) 3t\sqrt{3} - t can be rational or irrational, depending on the value of tt.
  1. Identify Type of Number: Identify whether 3\sqrt{3} is a rational or irrational number.\newlineSince 33 is not a perfect square, 3\sqrt{3} is an irrational number.
  2. Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational, depending on the specific values of those numbers.
  3. Analysis of Given Statements: Analyze the given statements with respect to the properties of irrational numbers.\newlineIf t=3t = \sqrt{3}, then 33=0\sqrt{3} - \sqrt{3} = 0, which is rational.\newlineIf tt is any irrational number other than 3\sqrt{3}, then 3t\sqrt{3} - t is irrational because the difference of two distinct irrational numbers is irrational.\newlineTherefore, 3t\sqrt{3} - t can be rational or irrational, depending on the value of tt.

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