{
  "title": "Operations on Real Numbers - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "√2 × √2 = ? ✖️", "options": {"A": "2", "B": "√4", "C": "4", "D": "√2"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Add: √3 + √3 = ? ➕", "options": {"A": "√6", "B": "2√3", "C": "√9", "D": "3"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "√8 ÷ √2 = ? ➗", "options": {"A": "√4", "B": "2", "C": "√6", "D": "4"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "(√5)² = ? 🔲", "options": {"A": "5", "B": "√25", "C": "25", "D": "√5"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Simplify: √9 × √4 = ?", "options": {"A": "√13", "B": "6", "C": "√36", "D": "12"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "What is √18 ÷ √2? 🤔", "options": {"A": "√9", "B": "3", "C": "√16", "D": "4"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "√50 - √2 = ? ➖", "options": {"A": "√48", "B": "4√2", "C": "5√2", "D": "3√2"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Multiply: √7 × √7 = ?", "options": {"A": "7", "B": "√49", "C": "14", "D": "49"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Add: 2√5 + 3√5 = ? ➕", "options": {"A": "5√5", "B": "6√5", "C": "5√10", "D": "√50"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "√12 × √3 = ?", "options": {"A": "√36", "B": "6", "C": "36", "D": "√15"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Simplify: √27 ÷ √3 = ?", "options": {"A": "√9", "B": "3", "C": "9", "D": "√24"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "2√6 × 3√6 = ? ✖️", "options": {"A": "6√6", "B": "36", "C": "12√6", "D": "6√12"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "√(1/4) = ? 🔳", "options": {"A": "1/2", "B": "2", "C": "√1/√4", "D": "0.5"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Subtract: 5√2 - 2√2 = ?", "options": {"A": "3√2", "B": "√2", "C": "7√2", "D": "3"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "√16 + √25 = ? ➕", "options": {"A": "9", "B": "√41", "C": "20", "D": "41"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "√(9/16) = ?", "options": {"A": "3/4", "B": "4/3", "C": "√3/√4", "D": "0.75"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Multiply: √3 × √12 = ?", "options": {"A": "√36", "B": "6", "C": "√15", "D": "36"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Add rational and irrational: 2 + √3 = ? ➕", "options": {"A": "Rational", "B": "Irrational", "C": "5", "D": "2√3"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "√(0.04) × √(0.25) = ?", "options": {"A": "0.1", "B": "0.2", "C": "0.3", "D": "0.01"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Divide: √45 ÷ √5 = ?", "options": {"A": "√9", "B": "3", "C": "9", "D": "√40"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Simplify: √8 + √18 = ? ➕", "options": {"A": "√26", "B": "5√2", "C": "13√2", "D": "√98"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "(√3 + √2)² = ? 🔲", "options": {"A": "5", "B": "3+2√6", "C": "5+2√6", "D": "6"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "√75 - √48 = ? ➖", "options": {"A": "√27", "B": "3√3", "C": "√3", "D": "9√3"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Multiply: (2+√3)(2-√3) = ? ✖️", "options": {"A": "1", "B": "4", "C": "4-3", "D": "7"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Rationalize: 1/√2 = ? 🔄", "options": {"A": "√2/2", "B": "0.5√2", "C": "√2", "D": "2/√2"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Simplify: √50 + √98 - √8 = ?", "options": {"A": "10√2", "B": "12√2", "C": "9√2", "D": "15√2"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "If a=√5, b=√20, then a×b = ?", "options": {"A": "√100", "B": "10", "C": "5", "D": "25"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "(√6 - √3)(√6 + √3) = ?", "options": {"A": "3", "B": "√3", "C": "6-3", "D": "√18-√9"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Divide: √128 ÷ √8 = ?", "options": {"A": "√16", "B": "4", "C": "16", "D": "√120"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Add: √(1.44) + √(0.64) = ?", "options": {"A": "2.0", "B": "1.8", "C": "2.2", "D": "1.6"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Rationalize denominator: 3/√5 = ?", "options": {"A": "3√5/5", "B": "√5/3", "C": "3√5", "D": "15/√5"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Simplify: (√7 - √5)(√7 + √5) = ?", "options": {"A": "2", "B": "√2", "C": "12", "D": "7-5"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "√200 - √50 = ? ➖", "options": {"A": "5√2", "B": "10√2", "C": "√150", "D": "√250"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Multiply: √(1/3) × √(1/12) = ?", "options": {"A": "1/6", "B": "√(1/36)", "C": "1/√36", "D": "All of these"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "(3√2)² = ? 🔲", "options": {"A": "18", "B": "9×2", "C": "6√2", "D": "12"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Add: 1/√2 + √2 = ?", "options": {"A": "3√2/2", "B": "√2", "C": "2√2", "D": "1.5√2"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "√0.09 + √0.16 = ?", "options": {"A": "0.5", "B": "0.7", "C": "0.3+0.4", "D": "0.12"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Simplify: √(a²b⁴) = ?", "options": {"A": "ab²", "B": "a²b²", "C": "|a|b²", "D": "√a b²"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "If x = √8, then x²/2 = ?", "options": {"A": "4", "B": "8", "C": "16", "D": "32"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Rationalize: 5/(√3 - 1) = ?", "options": {"A": "(5√3 + 5)/2", "B": "5(√3+1)/2", "C": "5√3+5", "D": "2.5(√3+1)"}, "correct_answer": "B"},

    {"id": 41, "difficulty": "hard", "question": "Simplify: (√5 + √3)/(√5 - √3) = ? 🔄", "options": {"A": "(8+2√15)/2", "B": "4+√15", "C": "(5+3)/2", "D": "√8"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "If a=2+√3, find 1/a.", "options": {"A": "2-√3", "B": "1/(2+√3)", "C": "2-√3 (after rationalization)", "D": "√3-2"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "hard", "question": "√(6+√(6+√(6+...))) = ? (infinite nested radical) ∞", "options": {"A": "2", "B": "3", "C": "√6", "D": "6"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "Simplify: √(11 - 2√30) = ?", "options": {"A": "√6 - √5", "B": "√5 - √6", "C": "√30", "D": "√11 - √30"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "If x = √7 + √6 and y = √7 - √6, then x² + y² = ? 🔲", "options": {"A": "26", "B": "28", "C": "24", "D": "30"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Rationalize: 1/(√5 + √2) = ?", "options": {"A": "(√5 - √2)/3", "B": "(√5 - √2)/7", "C": "√5 - √2", "D": "(√5+√2)/3"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Simplify: (√3 + 1)/(√3 - 1) + (√3 - 1)/(√3 + 1) = ?", "options": {"A": "2", "B": "4", "C": "2√3", "D": "4√3"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "If √x + √y = √(x+y+2√(xy)), then √12 + √27 = ?", "options": {"A": "√39", "B": "5√3", "C": "√75", "D": "13√3"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "Evaluate: √(5√(5√(5…))) = ? (infinite) ∞", "options": {"A": "5", "B": "√5", "C": "5^(2/3)", "D": "25"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Simplify: (√8 - √2)² = ?", "options": {"A": "6", "B": "2", "C": "4", "D": "8"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "If a = √2 + 1, then a² + 1/a² = ?", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Rationalize: (√a - √b)/(√a + √b) = ?", "options": {"A": "(a-b)/(a+b-2√ab)", "B": "(a-b)/(a+b)", "C": "(a+b-2√ab)/(a-b)", "D": "1"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "hard", "question": "Simplify: ∛(54) + ∛(16) = ?", "options": {"A": "5∛2", "B": "3∛2 + 2∛2", "C": "5∛2", "D": "∛70"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "If x = 3-2√2, find √x + 1/√x.", "options": {"A": "2", "B": "2√2", "C": "4", "D": "√2"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Simplify: √(4+2√3) = ?", "options": {"A": "√3 + 1", "B": "√3 - 1", "C": "2√3", "D": "√6"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "(√a + √b)² + (√a - √b)² = ?", "options": {"A": "2(a+b)", "B": "4√ab", "C": "2a+2b", "D": "2a+2b+4√ab"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Evaluate: (√10 - √5) / (√2 - 1) = ?", "options": {"A": "√5", "B": "√10", "C": "√2", "D": "5"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "If √(x+1) + √(x-1) = √(4x-1), find x.", "options": {"A": "5/4", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Simplify: ∛(√(64)) = ?", "options": {"A": "2", "B": "4", "C": "∛8", "D": "2^(4/3)"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Given √2 ≈ 1.414, √3 ≈ 1.732, find √6 + √8 - √12 ≈ ?", "options": {"A": "1.414", "B": "2.828", "C": "2.449", "D": "3.146"}, "correct_answer": "A"}
  ]
}