Previous

On this page you can investigate how to graph square roots and their products and sums on the number line.
In the construction background is Pythagorean theorem. For more details investigate the Square root spiral page.

Square roots of the natural numbers on a number line

Down applet shows how to mark square roots of the natural numbers on the number line.
Click the animation button in the left-down angle of the applet to start animation. Also, you can stop the animation by clicking the same button.
Instead of using animation button, you can click the 'steps' slider and push arrows → or ← on the keyboard more times.
Can you make this construction on the paper?

Made by Antonija Horvatek with the GeoGebra program

Negative square roots on a number line

Upper applet shows the constructions of √2, √3 etc. on the number line.
If you understood it, now it's easy to find -√2, -√3 etc. as well.
Investigate it in the applet below.

Made by Antonija Horvatek with the GeoGebra program

Numbers a√n on a number line

In down applet investigate how to find √n, 2√n, 3√n etc., and -√n, -2√n, -3√n etc. on the number line.
First choose the number n, and then use check boxes and sliders in the given order.
Can you make such constructions on the paper?

Made by Antonija Horvatek with the GeoGebra program

Sums and roots on a number line

Choose the values of the a, n and b sliders and notice how to construct the given number on the number line. All the time you can change the values of the a, n and b sliders.
If needed, use the 'unit segment' slider to zoom the number line and move the origin point.

Made by Antonija Horvatek with the GeoGebra program

Can you make such constructions on the paper?
E.g. try to construct 3√2-5, -√3-1, -2√5+6 and √8+2.
You can use the applet to check yout constructions.

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.