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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 | |
| = x |
Therefore a is equal to √x.