Simplifying Square Roots

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Students will be able to simplify radicals.

Big Idea

Area models introduce this Common Core transitional lesson on simplifying square roots.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations.. The Video Narrative specifically explains this lesson’s Warm Up- Simplifying Radicals, which asks students to determine which of five square roots is about equivalent to 6.2

I also use this time to correct and record any past Homework.

Simplifying Radicals

37 minutes

This lesson builds on prior knowledge from eight grade Common Core and the ability to simplify radicals is an important skill needed for working with polynomial equations.  Therefore, I am spending this day ensuring that all my students are on the same page.  I introduce this from the concept of the area of a square.  This visual representation connects the students to the fact that a root is a physical number rather than an abstract concept.   We begin with a square with an integer side length and then move to a square with a radical side length.  We estimate this as a decimal and then look at it in “simplified” form. 

One important note here is that many of the processes that we have called simplification in algebra are looked at more as an equivalent form in the Common Core.  The “simplest” form varies depending on the context.  For example, √20 may be the most meaningful solution in some instances while 4.5 or 2√5 may make more sense in others (Math Practice 5).  This is an important conversation that needs to take place with students.

We practice simplifying non-perfect square roots, starting with numbers and then adding in variables, and finishing with rationalizing the denominator. 

Please see the PowerPoint for detailed presentation notes.                

Exit Ticket

3 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's exit ticket asks students to simplifying a square root.  


The first eight problems are a reinforcement of the day’s lesson.  It is important that students feel confident approaching problems like these and a certain amount of practice can go a long way to help this.  The final two problems are a bit of a stretch as I ask the students to identify a decimal approximation of a non-perfect square root without the use of a calculator and then explain their process.  While this was a discussion during the lesson, it wasn’t discretely practiced.  Students will need to stretch their understanding (Math Practice 1).  

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