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
1. Let line segment AB be unity (a line segment of length 1).
2. Construct √2 using AB as unity. Label the end point of this segment C.How?
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.

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