We all know that the square root of $2$ is an irrational number. That is to say, it cannot be written as a fraction $p/q$. Here $p$ and $q$ are integers, and $q$ is not zero. But it can be written in the form of a 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.
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.