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The number t t is irrational. Which statement about t47 t - \sqrt{47} is true?\newlineChoices:\newline(A) t47 t - \sqrt{47} is rational. \newline(B) t47 t - \sqrt{47} is irrational. \newline(C) t47 t - \sqrt{47} can be rational or irrational, depending on the value of t t .

Full solution

Q. The number t t is irrational. Which statement about t47 t - \sqrt{47} is true?\newlineChoices:\newline(A) t47 t - \sqrt{47} is rational. \newline(B) t47 t - \sqrt{47} is irrational. \newline(C) t47 t - \sqrt{47} can be rational or irrational, depending on the value of t t .
  1. Identify Nature of 47\sqrt{47}: 47\sqrt{47} is the square root of a non-perfect square, which means it is an irrational number.
  2. Consider Subtraction of Irrational Numbers: Consider the subtraction of two irrational numbers.\newlineThe difference between two irrational numbers can be either rational or irrational. It is not possible to determine the nature of t47t - \sqrt{47} without knowing the specific value of tt.
  3. Analyze Given Choices: Analyze the given choices in relation to the subtraction of irrational numbers. \newlineIf tt were specifically chosen to be 47\sqrt{47}, then t47t - \sqrt{47} would be 00, which is rational. \newlineHowever, if tt is any other irrational number, t47t - \sqrt{47} could still be irrational. \newline
  4. Final answer: Therefore, the statement that t47t - \sqrt{47} can be rational or irrational, depending on the value of tt, is true.

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