Construct the Square Root of 6

This construction uses the constructions of √2 and √3. The algebraic formula is (√2)2 X (√3)2 = (√6)2.

DiagramInstructions
Line segment with ends labeled 'A' and 'B'. 1. Let line segment AB be unity (a line segment of length 1).
Line segment with ends labeled 'A' and 'B', circle with center at 'B' and radius of AB, line through 'B' perpendicular to the line segment AB, intersection of the perpendicular line and the circle is labeled 'C', segment connecting 'C' and 'A' has a length square root of 2. 2. Construct √2 using AB as unity. Label the end point of this segment C. How?
Previous image plus circle with center at 'C' with a radius of AC, the two circles intersect at 'B' and 'C prime'. The length of 'C prime' is square root of 6. 3. Construct √3 using AC as a base. The segment C'D is of length √6. How?

You can change the figure by clicking and dragging on points A and B. Notice that while the measure of the length of AB changes, the ratio of the length of C'E to AB is always √5.

Proof

  1. The length of AB is taken to be 1 by definition.
  2. By construction, the length of AC is √2.
  3. By construction, the length of C'D is √3 X √2 = √6.

Citation

Cite this article as:
McAdams, David, "Construct the Square Root of 6", from LifeIsAStoryProblem.org, 30 June 2007, , URL https://lifeisastoryproblem.tripod.com/numbers/cons_sqrt_6.html.

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