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    Question

    A number exceeds its square root by 30. What is the

    number?
    A 10 Correct Answer Incorrect Answer
    B 25 Correct Answer Incorrect Answer
    C 36 Correct Answer Incorrect Answer
    D 45 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the number be 'x'.

    So, x - √x = 30

    On squaring both sides, we get:

    (x - √x)² = 30²

    ⇒ x² + x - 2x√x = 900

    Now, let’s simplify:

    (x - 30)² = x

    ⇒ x² - 60x + 900 = x

    ⇒ x² - 61x + 900 = 0

    ⇒ x² - 25x - 36x + 900 = 0

    ⇒ x(x - 25) - 36(x - 25) = 0

    ⇒ (x - 36)(x - 25) = 0

    So, x = 36 or x = 25

    Only x = 36 satisfies the original equation

    Hence, the number is 36

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