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 )

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Remark :

9025 = 5 * 5 * 19 * 19

9025 = 5 ^ 2 * 19 ^ 2
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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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