Frequently Asked Questions
How do you use geometry to square root a number?
Begin with a segment equal in length to the number, x and extend the length by one unit. Use this new length as a diameter to produce a semicircle. Construct a perpendicular to the diameter at the unit mark and allow the perpendicular to intersect the semicircle, the length of the new segment will be √x.
We can prove this as follows.
The diameter is x + 1 and as c is equal to the radius, c = ½(x + 1). Hence b = ½(x 1).
Using the Pythagorean Theorem,
|a²||= c² b²|
|= ¼(x + 1)² ¼(x 1)²|
|= ¼(x² + 2x + 1) ¼(x² 2x + 1)|
|= ¼ × 4x|
Therefore a is equal to √x.