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Investigation

How to draw a line segments whose lenghts are √2, √3 etc.?
Find an answer in the applet below. Follow the instructions in the applet.

Made by Predrag Brkić i Antonija Horvatek with the GeoGebra program

Can you repeat the construction from the applet on the paper?
Can you draw a line segment whose lenght is √2 cm ? What about √5 dm ?

The upper applet construction is known as 'Square root spiral'. We can continue it, look at down applet...

Square root spiral

In this applet you can see the square root spiral construction.
Move the 'n' slider to construct line segments whose lenghts are square roots of the natural numbers.

Made by Predrag Brkić i Antonija Horvatek with the GeoGebra program

Check your understanding

In down applet, vertical cathetus lenght is equal 1, and horizontal cathetus lenght is sqare root of some natural number.
Can you say in a moment what is hypotenuse lenght? Check your answer by clicking the 'solution' check box.
Can you recognize if triangle from the applet below is part of the construction from upper applet? Is there some connection?

Made by Antonija Horvatek with the GeoGebra program

Notice:
What is the difference between down applet and upper applet?
Can you say the value of the x in down applet, as well?
Check your answer by clicking the 'solution' check box.

Made by Antonija Horvatek with the GeoGebra program

The last applet explains the construction of square roots on the number line.
Let's see it; click down link to the next page.

Note:

If applets don't work correctly, try to use another web browser (Chrome, Mozilla Firefox, Internet Explorer...) or change some properties in the web browser you use. Also, you can try upgrade your web browser.