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The number b b is rational. Which statement about b3 b - \sqrt{3} is true?\newlineChoices:\newline(A) b3 b - \sqrt{3} is rational.\newline(B) b3 b - \sqrt{3} is irrational.\newline(C) b3 b - \sqrt{3} can be rational or irrational, depending on the value of b b .

Full solution

Q. The number b b is rational. Which statement about b3 b - \sqrt{3} is true?\newlineChoices:\newline(A) b3 b - \sqrt{3} is rational.\newline(B) b3 b - \sqrt{3} is irrational.\newline(C) b3 b - \sqrt{3} can be rational or irrational, depending on the value of b b .
  1. Identify Type of Number: Identify whether 3\sqrt{3} is a rational or irrational number.\newlineSince 33 is a non-perfect square, 3\sqrt{3} is an irrational number.
  2. Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.
  3. Apply Property: Apply the property to the given problem.\newlineSince bb is rational and 3\sqrt{3} is irrational, b3b - \sqrt{3} must be irrational.

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