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The number bb is rational. Which statement about 44b\sqrt{44} - b is true?\newlineChoices:\newline(A) 44b\sqrt{44} - b is rational.\newline(B) 44b\sqrt{44} - b is irrational.\newline(C) 44b\sqrt{44} - b can be rational or irrational, depending on the value of bb.

Full solution

Q. The number bb is rational. Which statement about 44b\sqrt{44} - b is true?\newlineChoices:\newline(A) 44b\sqrt{44} - b is rational.\newline(B) 44b\sqrt{44} - b is irrational.\newline(C) 44b\sqrt{44} - b can be rational or irrational, depending on the value of bb.
  1. Identify Non-Perfect Square: We know that the square root of a non-perfect square is irrational. The number 4444 is not a perfect square, so 44\sqrt{44} is irrational.
  2. Subtract Rational from Irrational: Since bb is given to be rational, subtracting a rational number (bb) from an irrational number (44\sqrt{44}) will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.
  3. Final Result: Therefore, 44b\sqrt{44} - b is irrational, which corresponds to choice (B).

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