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    Question

    If √̅1̅2̅-̅2̅√̅3̅5̅ +

    √̅8̅+̅2̅√̅1̅5̅ = √a + √b, where a and b are positive integers, then the value of b – a is closest to:
    A -5 Correct Answer Incorrect Answer
    B -3 Correct Answer Incorrect Answer
    C -2 Correct Answer Incorrect Answer
    D -4 Correct Answer Incorrect Answer

    Solution

    √ (12 - 2√35) + √(8 + 2 √15) = ( √a + √b) => √ (√7 - √5)2 + √( √3 + √5)2 = ( √a + √b) => √7 - √5 + √3 - √5 = ( √a + √b) => = ( √a + √b) = √7 + √3 => a = 7 and b = 3 The value of b – a = 3 - 7 = -4

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