Geometry

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A square has a side length of 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

  • Geometry -

    Pitagorin teorem:

    diagonal = sqrt ( 95 ^ 2 + 95 ^ 2 )

    diagonal = sqrt ( 2 * 9025 )

    ----------------------
    Remark :

    9025 = 5 * 5 * 19 * 19

    9025 = 5 ^ 2 * 19 ^ 2
    ----------------------

    diagonal = sqrt ( 2 * 9025 )

    diagonal = sqrt ( 2 * 5 ^ 2 * 19 ^ 2 )

    diagonal = 5 * 19 * sqrt ( 2 )

    diagonal = 95 * sqrt ( 2 )

  • Geometry -

    diagonal = sqrt ( 95 ^ 2 + 95 ^ 2 )

    diagonal = sqrt ( 2 * 95 ^ 2 )

    diagonal = sqrt ( 2 * 9025 )

  • Geometry -

    d = sqrt ( 95 ^ 2 + 95 ^ 2 )

    d = sqrt ( 2 95 ^ 2 )

    d = sqrt ( 95 ^ 2 ) * sqrt ( 2 )

    d = 95 sqrt ( 2 )

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