This video lesson serves two main purposes: to reiterate that some solutions to quadratic equations are irrational, and to give students the tools to express those solutions exactly and succinctly.

Students recall that the radical symbol (√) can be used to denote the positive square root of a number. Many quadratic equations have a positive and a negative solution, and up until this point, students have been writing them separately. Here, students are introduced to the plus-minus symbol (±) as a way to express both solutions.

Students also briefly recall the meanings of rational and irrational numbers. They see that sometimes the solutions are expressions that involve a rational number and an irrational number—for example, x = ±√8 + 3.

Students make sense of these solutions by finding their decimal approximations and by solving the equations by graphing. The work here gives students opportunities to reason quantitatively and abstractly (MP2).

Algebra 1, Episode 22: Unit 7, Lesson 15 | Illustrative Math