Du Plantier's Square Root Extractor

move along x axis

move along y axis

8

The square root of 9 is 3; the approximation is 3.

This Demonstration shows square root extraction based on the identity

2

(n+1)

-

2

(n-1)

=4n

. For example, to find the square root of 9, move along the

y

axis to

9-1=8

and along the

x

axis until the

9+1=10

mark on the sloping line is on the

x

axis. The

x

intercept of the sloping line will be

2

9

=6

if measured in the same units as the

y

axis and the sloping line. If we scale the

x

axis in a

1:2

ratio with the

y

axis, then the

x

intercept will be at

9

=3

.