Use a square a mechanism to calculate #sqrt(2)# geometrically?

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1 Answer
Shwetank Mauria
Jan 10, 2017

Please see below.

Explanation:

Draw a line #AD# equal to one unit.

Draw a perpendicular #DC# on #D# (as shown in above image), where #DC# is again one unit.

Join #AC#. It is equal to #sqrt2# units.
enter image source here
as according to Pythagoras theorem,

#AC^2=AD^2+DC^2=1^2+1^2=1+1=2#

Hence, #AC=sqrt2# units.

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