Students will learn what the product property for square roots is, and how to use it. They'll start by simplifying expressions like \(\sqrt{8} \cdot \sqrt{10},\) then move on to expressions like \(3\sqrt{2x} \cdot 4\sqrt{10x}.\) After that, students will combine their skill of distributing with their skill of using the product property. They'll solve problems such as

$$\sqrt{2}\left(x + \sqrt{7}\right)$$Next, students will combine their skill of FOILing, or repeatedly distributing, with their skill of using the product property. They'll solve problems like

$$\left(\sqrt{2} + \sqrt{7}\right)\left(\sqrt{2} + \sqrt{5}\right)$$Next, give your students these challenges:

Conclude by leading this investigation:

Irreptiles (proportion, similar shapes)

by MathPickle