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

Jan 10, 2017

#### Explanation:

Draw a line $A D$ equal to one unit.

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

Join $A C$. It is equal to $\sqrt{2}$ units.

as according to Pythagoras theorem,

$A {C}^{2} = A {D}^{2} + D {C}^{2} = {1}^{2} + {1}^{2} = 1 + 1 = 2$

Hence, $A C = \sqrt{2}$ units.