I started in on a new section with my younger son yesterday – square roots.

We have, of course, talked about square roots informally through the various projects that we do, but we have not discussed properties of square roots in detail until now. It is always really interesting to me to see the initial reactions that the boys have to these new subjects.

The first discussion today was about some basic properties that he already knew, and then I threw in a few twists. The idea that a square root has to be non-negative caused a little confusion. We ended up with a short discussion of .

Next up was today’s lesson about finding square roots of large integers. I enjoyed his approach to the specific problem below, and think that the time that we spent in the first half of this school year studying number theory has helped him become comfortable with this type of problem.

I found his explanation of why you take half of a power when you take a square root to be really fascinating.

So, a nice start to our new chapter on square roots, and nice to see a little bit of the work we did in the *Introduction to Number Theory* book paying off.