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Which two integers is 66-\sqrt{66} between?\newlineChoices:\newline(A) 8-8 and 7-7\newline(B) 12-12 and 11-11\newline(C) 9-9 and 8-8\newline(D) 11-11 and 10-10

Full solution

Q. Which two integers is 66-\sqrt{66} between?\newlineChoices:\newline(A) 8-8 and 7-7\newline(B) 12-12 and 11-11\newline(C) 9-9 and 8-8\newline(D) 11-11 and 10-10
  1. Identify Perfect Squares: Step 11: Identify the perfect squares close to 6666. The perfect square just below 6666 is 6464. The perfect square just above 6666 is 8181.
  2. Calculate Square Roots: Step 22: Calculate the square roots of these perfect squares.\newline64=8\sqrt{64} = 8 because 8×8=648 \times 8 = 64.\newline81=9\sqrt{81} = 9 because 9×9=819 \times 9 = 81.
  3. Determine Negative Square Roots: Step 33: Determine the negative square roots.\newline64=8.-\sqrt{64} = -8.\newline81=9.-\sqrt{81} = -9.
  4. Place 66-\sqrt{66}: Step 44: Place 66-\sqrt{66} in the correct interval.\newlineSince 9<66<8-9 < -\sqrt{66} < -8, 66-\sqrt{66} is between 9-9 and 8-8.

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