Square root

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The roots √1 , √2 , √3 , √4 ... can be generated using the Pythagorean theorem.

The drawing shows the development of these roots.

√4

√1

√3

√2

1

1

1

The Pythagorean theorem gives in each case

1^² + √1^² = √2^²
1^² + √2^² = √3^²
1^² + √3^² = √4^²

The general rule is

1^² + √n − 1^² = √n^²