• If \( \Large \sqrt{2} \) = 1.4142, then the value of \( \Large \frac{7}{4 + \sqrt{2}} \) is

    A) 3.5858

      B) 4.4142

    C) 1.2929

      D) 1.5858

    Correct Answer:
    C) 1.2929

    Description for Correct answer
    \( \Large \frac{7}{4+\sqrt{2}} = \frac{7}{4+\sqrt{2}} \times \frac{ \left(4 - \sqrt{2}\right) }{ \left(4 - \sqrt{2}\right) } \)

    = \( \Large \frac{7 \left(4-\sqrt{2}\right) }{16 - 2} \)

    \( \Large Because \left(a+b\right) \times \left(a-b\right) = a^{2} - b^{2} \)

    = \( \Large \frac{7 \left(4-\sqrt{2}\right)}{14} = \frac{4-\sqrt{2}}{2} = \frac{4-1.4142}{2} \)

    = \( \Large \frac{2.5858}{2} = 1.2929 \)

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