Students will learn how to simplify the square root of a rational expression. One prereq is being able to simplify the square root of a monomial. Next, challenge your students to derive the height formula for an equilateral triangle. This formula is a consequence of the Pythagorean theorem, the power of a quotient rule for exponents, taking the square root of both sides, and simplifying the square root of a rational expression. The derivation can be seen here. Finally, give your students this challenge: In the figure below, the circle has area \(9\pi.\) Find the side length of the equilateral triangle.
The solution can be found easily by using the area formula for a circle to find the radius of the circle, doubling this value to find the height of the equilateral triangle, then using the formula for the height of an equilateral triangle to find its side length.
TODO: Simplifying square roots of radical expressions (cube root, etc.)?