# A Construction of the Square Root of Seven

A Construction of the Square Root of Seven

This Demonstration shows a construction of and such that .

a

r

r/a=

7

Construction

Step 1: Draw a segment of length . Divide it by a point giving the ratio .

OB

r

P

5:2

Step 2: Draw an equilateral triangle .

PQB

Step 3: Let be the intersection of a line through that is parallel to and a line through that is perpendicular to .

A

Q

OQ

P

OB

Step 4: Let . Then and have the required property.

a=AB

a

r

Verification

PA==

2

7

r

3

2

r

3

7

Thus

a=PA+PB=+=

2

2

2

3r

2

49

4r

2

49

r

2

7