Irrational Numbers on a Number Line

With this simple interactive, in Irrational Numbers for Grade 8 (Chrome and Desktop), we explore the approximate locations of square roots on a number line, following the method shown in the introductory video.

The red dots below indicate the locations of integer square roots, from \(\mathtt{\sqrt{2}}\) to \(\mathtt{\sqrt{20}}\), skipping over the square roots of the perfect squares.

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The task here involves positioning the right triangle (then click) so that the hypotenuse forms the radius of a circle which intersects the number line at each square root. Explaining one's thinking is key here, of course. If it weren't for the thinking, it would be much more boring than it already is.