Geometry
posted by Cassie on .
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.

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 ) 
diagonal = sqrt ( 95 ^ 2 + 95 ^ 2 )
diagonal = sqrt ( 2 * 95 ^ 2 )
diagonal = sqrt ( 2 * 9025 ) 
d = sqrt ( 95 ^ 2 + 95 ^ 2 )
d = sqrt ( 2 95 ^ 2 )
d = sqrt ( 95 ^ 2 ) * sqrt ( 2 )
d = 95 sqrt ( 2 )