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The number qq is irrational. Which statement about q−39q - \sqrt{39} is true?\newlineChoices:\newline(A) q−39q - \sqrt{39} is rational.\newline(B) q−39q - \sqrt{39} is irrational.\newline(C) q−39q - \sqrt{39} can be rational or irrational, depending on the value of qq.

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Q. The number qq is irrational. Which statement about q−39q - \sqrt{39} is true?\newlineChoices:\newline(A) q−39q - \sqrt{39} is rational.\newline(B) q−39q - \sqrt{39} is irrational.\newline(C) q−39q - \sqrt{39} can be rational or irrational, depending on the value of qq.
  1. Identify Type of Number: Identify whether 39\sqrt{39} is a rational or irrational number.3939 is a non-perfect square.39\sqrt{39} is an irrational number.
  2. Properties of Irrational Numbers: Consider the properties of irrational numbers. The sum or difference of a rational number and an irrational number is always irrational. The sum or difference of two irrational numbers can be rational or irrational.
  3. Analyze Expressions with Scenarios: Analyze the given expressions with different scenarios.\newlineIf qq is an irrational number not related to 39\sqrt{39}, then q−39q - \sqrt{39} would be irrational.\newlineIf q=39q = \sqrt{39}, then 39−39=0\sqrt{39} - \sqrt{39} = 0, which is rational.\newlineTherefore, q−39q - \sqrt{39} can be rational or irrational, depending on the value of qq.

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