**continued fraction**.

Here is how you can discover the continued fraction representation of the square root of $2$. You will need a calculator to do the calculations. Carefully understand the following calculations.

Note that the $.41421\dots $ starts repeating, and we get a fraction that looks like

You can chop off the fraction at any point and get a fraction that is approximately equal to the square root of $2$.

As for this week’s activity, do a similar calculation (using a calculator) for the square root of $3$ and the square root of $5$ and find the continued fraction representation of these irrational numbers.