{
  "title": "Cube Roots by Estimation - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "The cube root of 8 is? 🧊",
      "options": { "A": "2", "B": "4", "C": "16", "D": "64" },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Estimate ∛27. It is between which consecutive integers? 📏",
      "options": {
        "A": "3 and 4",
        "B": "2 and 3",
        "C": "1 and 2",
        "D": "4 and 5"
      },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "∛64 is? ✨",
      "options": { "A": "4", "B": "8", "C": "16", "D": "32" },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Cube root of 1 is? ✅",
      "options": { "A": "1", "B": "0", "C": "3", "D": "1/3" },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "∛125 is? 🎯",
      "options": { "A": "5", "B": "25", "C": "15", "D": "10" },
      "correct_answer": "A"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Which integer's cube is 216? 🔢",
      "options": { "A": "6", "B": "12", "C": "36", "D": "18" },
      "correct_answer": "A"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "Cube root of 1000 is? ➡️",
      "options": { "A": "10", "B": "100", "C": "30", "D": "300" },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "∛343 = ? (Hint: 7³) 🧮",
      "options": { "A": "7", "B": "49", "C": "21", "D": "14" },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Which is the perfect cube? 🧊",
      "options": { "A": "8", "B": "10", "C": "12", "D": "18" },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Estimate ∛50. It lies between? 🔍",
      "options": {
        "A": "3 and 4",
        "B": "4 and 5",
        "C": "2 and 3",
        "D": "5 and 6"
      },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Cube of 0.2 is 0.008. So ∛0.008 = ? 🎲",
      "options": { "A": "0.2", "B": "0.02", "C": "0.4", "D": "0.04" },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "∛(-27) is? ❄️",
      "options": { "A": "-3", "B": "3", "C": "-9", "D": "9" },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Which number's cube is 0.125? 📐",
      "options": { "A": "0.5", "B": "0.05", "C": "0.25", "D": "0.2" },
      "correct_answer": "A"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "Estimate ∛200. Between which integers? 🚧",
      "options": {
        "A": "5 and 6",
        "B": "6 and 7",
        "C": "4 and 5",
        "D": "7 and 8"
      },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "∛(1/8) = ? 🍰",
      "options": { "A": "1/2", "B": "1/4", "C": "2", "D": "4" },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Cube root of 512 is? 🧠",
      "options": { "A": "8", "B": "16", "C": "64", "D": "32" },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "Which is NOT a perfect cube? 🚫",
      "options": { "A": "100", "B": "27", "C": "125", "D": "64" },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Estimate ∛2. It is between? 🔢",
      "options": {
        "A": "1 and 2",
        "B": "0 and 1",
        "C": "2 and 3",
        "D": "3 and 4"
      },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "If n³ = 729, then n = ? ⚡",
      "options": { "A": "9", "B": "27", "C": "81", "D": "3" },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Cube root of 0.064 is? 🎪",
      "options": { "A": "0.4", "B": "0.04", "C": "0.8", "D": "0.08" },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Estimate ∛150 to nearest whole number. 📊",
      "options": { "A": "5", "B": "6", "C": "4", "D": "7" },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "∛(27/125) = ? ➗",
      "options": { "A": "3/5", "B": "5/3", "C": "9/25", "D": "25/9" },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Which is greater? ∛64 or ∛125? ⬆️",
      "options": {
        "A": "∛125",
        "B": "∛64",
        "C": "Equal",
        "D": "Cannot compare"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Estimate ∛500. It's between which two consecutive integers? 🚀",
      "options": {
        "A": "7 and 8",
        "B": "8 and 9",
        "C": "6 and 7",
        "D": "9 and 10"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "If cube of a number is 0.001, the number is? 🧩",
      "options": { "A": "0.1", "B": "0.01", "C": "0.001", "D": "0.0001" },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "∛(216/1000) simplifies to? ✂️",
      "options": { "A": "6/10", "B": "3/5", "C": "0.6", "D": "All of these" },
      "correct_answer": "D"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "By estimation, ∛300 is closest to? 🎯",
      "options": { "A": "6.7", "B": "6.5", "C": "7", "D": "6" },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Cube root of -512 is? ➖",
      "options": { "A": "-8", "B": "8", "C": "-64", "D": "64" },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Estimate ∛2.744 (Hint: 14³=2744) 🔍",
      "options": { "A": "1.4", "B": "14", "C": "0.14", "D": "140" },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Which is smaller? ∛8 or ∛27? ⬇️",
      "options": { "A": "∛8", "B": "∛27", "C": "Equal", "D": "Cannot say" },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "∛(0.000729) = ? (Hint: 9³=729) 🧊",
      "options": { "A": "0.09", "B": "0.9", "C": "0.009", "D": "0.0009" },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Cube root of 15.625 is? (Hint: 25³=15625) 🧮",
      "options": { "A": "2.5", "B": "25", "C": "0.25", "D": "250" },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "If ∛x = 0.3, then x = ? 🔄",
      "options": { "A": "0.027", "B": "0.27", "C": "0.09", "D": "0.9" },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "By estimation, ∛8000 is? 🚅",
      "options": { "A": "20", "B": "200", "C": "40", "D": "80" },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "∛(-1/64) = ? ❄️",
      "options": { "A": "-1/4", "B": "1/4", "C": "-1/8", "D": "1/8" },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Between which integers does ∛95 lie? 🔢",
      "options": {
        "A": "4 and 5",
        "B": "5 and 6",
        "C": "3 and 4",
        "D": "6 and 7"
      },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Cube root of (8 × 27) = ∛8 × ∛27? ✅",
      "options": {
        "A": "True",
        "B": "False",
        "C": "Sometimes",
        "D": "Cannot say"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "Estimate ∛0.5. It's between? 📏",
      "options": {
        "A": "0.7 and 0.8",
        "B": "0.8 and 0.9",
        "C": "0.5 and 0.6",
        "D": "0 and 0.5"
      },
      "correct_answer": "A"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "If n is an integer, ∛(n³ + 1) is approximately? 🎲",
      "options": { "A": "n", "B": "n+1", "C": "n³", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "∛(1000000) = ? 🌟",
      "options": { "A": "100", "B": "1000", "C": "10", "D": "10000" },
      "correct_answer": "A"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Estimate ∛17576 without calculator. (Hint: 26³=17576) 🧠",
      "options": { "A": "26", "B": "36", "C": "16", "D": "46" },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "∛(0.004096) = ? (Hint: 16³=4096) 🎯",
      "options": { "A": "0.16", "B": "1.6", "C": "0.016", "D": "16" },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "If ∛(3.375) = 1.5, then ∛(3375) = ? 🔥",
      "options": { "A": "15", "B": "150", "C": "1.5", "D": "0.15" },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Estimate ∛(250047). Closest integer? (Hint: 63³=250047) ⚡",
      "options": { "A": "63", "B": "64", "C": "62", "D": "65" },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "∛(12167) = ? (Hint: 23³=12167) 🚀",
      "options": { "A": "23", "B": "13", "C": "33", "D": "43" },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "Which is correct? ∛(a+b) = ∛a + ∛b? 🧩",
      "options": { "A": "No", "B": "Yes", "C": "Sometimes", "D": "If a=b" },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Estimate ∛(300763). (Hint: 67³=300763) 📊",
      "options": { "A": "67", "B": "57", "C": "77", "D": "87" },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "If ∛(x) = 2.5, then x is between? 📈",
      "options": {
        "A": "15 and 16",
        "B": "14 and 15",
        "C": "16 and 17",
        "D": "2 and 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "∛(0.000000125) = ? (Hint: 5³=125) 🧮",
      "options": { "A": "0.005", "B": "0.05", "C": "0.0005", "D": "0.5" },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Estimate ∛(970299). (Hint: 99³=970299) 🎲",
      "options": { "A": "99", "B": "89", "C": "109", "D": "79" },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "∛(42875) = ? (Hint: 35³=42875) 🔢",
      "options": { "A": "35", "B": "25", "C": "45", "D": "55" },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "If cube of a two-digit number ends in 7, its cube root ends in? 🎯",
      "options": { "A": "3", "B": "7", "C": "9", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Estimate ∛(592704). (Hint: 84³=592704) 🚧",
      "options": { "A": "84", "B": "74", "C": "94", "D": "64" },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "∛(0.046656) = ? (Hint: 36³=46656) ✨",
      "options": { "A": "0.36", "B": "3.6", "C": "0.036", "D": "36" },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "If ∛(9261) = 21, then ∛(9.261) = ? 🔄",
      "options": { "A": "2.1", "B": "0.21", "C": "21", "D": "0.021" },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "By estimation, ∛(110592) = ? (Hint: 48³=110592) 🏆",
      "options": { "A": "48", "B": "38", "C": "58", "D": "28" },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "∛(-0.027) = ? ❄️",
      "options": { "A": "-0.3", "B": "0.3", "C": "-0.03", "D": "-0.003" },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Estimate ∛(884736). (Hint: 96³=884736) 🚀",
      "options": { "A": "96", "B": "86", "C": "106", "D": "76" },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "If ∛(a) = 0.07, then a = ? 🔍",
      "options": {
        "A": "0.000343",
        "B": "0.343",
        "C": "0.0343",
        "D": "0.00343"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "∛(79507) = ? (Hint: 43³=79507) ✅",
      "options": { "A": "43", "B": "33", "C": "53", "D": "23" },
      "correct_answer": "A"
    }
  ]
}