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Which two integers is 123–\sqrt{123} between?\newlineChoices:\newline(A)11–11 and 10–10\newline(B)10–10 and 9–9\newline(C)12–12 and 11–11\newline(D)14–14 and 13–13

Full solution

Q. Which two integers is 123–\sqrt{123} between?\newlineChoices:\newline(A)11–11 and 10–10\newline(B)10–10 and 9–9\newline(C)12–12 and 11–11\newline(D)14–14 and 13–13
  1. Identify Perfect Squares: Identify the perfect squares around 123123. The perfect square just below 123123 is 121121 (11211^2). The perfect square just above 123123 is 144144 (12212^2).
  2. Calculate Square Roots: Calculate the square roots of 121121 and 144144.121=11\sqrt{121} = 11144=12\sqrt{144} = 12
  3. Determine Negative Square Roots: Determine the negative square roots.\newline121=11-\sqrt{121} = -11\newline144=12-\sqrt{144} = -12
  4. Place Negative Square Roots: Place 123-\sqrt{123} within the correct interval.\newlineSince 12<123<11-12 < -\sqrt{123} < -11, 123-\sqrt{123} is between 12-12 and 11-11.

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