Square Root of a Sum? - Geometric Interpretation

We know that for non-negative numbers  Can we apply the same for the sum? 
In the example below a and b are the legs of a right triangle.  According to the Pythagorean Theorem the hypotenuse is

• Drag to the left the blue point A to rotate the leg AC around point C until the two legs form one segment.
  
• Drag to the left the orange point A to rotate the hypotenuse around point B until it comes to the base of the triangle.
• Compare the lengths  

Irina Boyadzhiev, 6 April 2013, Created with GeoGebra

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Geometric representation of the sum of two radicals

This activity is part of the lesson on adding radicals posted at Mathematics for Teaching.

How to construct the figure:

Use the regular polygon tool. Click on two points (endpoints of the diagonal of 2 by 1 unit square in the grid). From then on just click on the diagonals each time to generate the squares.

To type the radical, use the text tool, click anywhere on the grid, check latex in the dialogue window and type \sqrt{5} and you're done.

To change the color, right click on the figure, click color, choose and you're done.

When you are ready click on the file menu and choose new. This will give you a brand new grid to practice constructing the figure.





















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