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Which lists contain only rational numbers? Select all that apply.\newlineMulti-select Choices:\newline(A) 6-6, 7-7, 9-9, 11-11, 6161\newline(B) 6\sqrt{6}, 12\sqrt{12}, 18\sqrt{18}, 24\sqrt{24}, 30\sqrt{30}\newline(C) 7-700, 7-711, 7-722, 7-733, 7-744\newline(D) 7-755, 7-766, 7-777, 7-788\newline(E) 7-799, 9-900, 9-911, 9-922

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Q. Which lists contain only rational numbers? Select all that apply.\newlineMulti-select Choices:\newline(A) 6-6, 7-7, 9-9, 11-11, 6161\newline(B) 6\sqrt{6}, 12\sqrt{12}, 18\sqrt{18}, 24\sqrt{24}, 30\sqrt{30}\newline(C) 7-700, 7-711, 7-722, 7-733, 7-744\newline(D) 7-755, 7-766, 7-777, 7-788\newline(E) 7-799, 9-900, 9-911, 9-922
  1. Analyze Integers: Step 11: Analyze list AA 6,7,9,11,61-6, -7, -9, -11, 61. All numbers in this list are integers. Integers are rational numbers because they can be expressed as a fraction where the denominator is 11 (e.g., 6-6 can be written as 61-\frac{6}{1}).
  2. Analyze Square Roots: Step 22: Analyze list (B) 6\sqrt{6}, 12\sqrt{12}, 18\sqrt{18}, 24\sqrt{24}, 30\sqrt{30}. Square roots of non-perfect squares are irrational numbers. None of 66, 1212, 1818, 2424, 3030 are perfect squares, so their square roots are irrational.
  3. Analyze Fractions: Step 33: Analyze list (C) 63\frac{6}{3}, 47\frac{4}{7}, 1199\frac{11}{99}, 613\frac{-6}{13}, 1337\frac{-13}{37}. All elements are fractions of integers. Fractions of integers are rational numbers as they can be expressed as a ratio of two integers.
  4. Analyze Decimals: Step 44: Analyze list (D) 0.8650.865, 0.44440.4444, 6.37-6.37, 11.11-11.11. All numbers are decimals. 0.8650.865 and 6.37-6.37 are terminating decimals; 0.44440.4444 and 11.11-11.11 are repeating decimals. Both terminating and repeating decimals are rational numbers.
  5. Analyze Repeating Decimals: Step 55: Analyze list (E) 7.{3}7.\{3\}, 4.1{5}4.1\{5\}, 6.{26}-6.\{26\}, 9.{1}-9.\{1\}. These are non-terminating, repeating decimals (indicated by the notation {}\{ \}). Non-terminating, repeating decimals are rational numbers.

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