How To Teach Math - Algebra 1

The Ultimate Math Teacher Resource

Resources

- Simplifying Square Roots - This worksheet is designed to be used in conjunctions with a lesson on simplifying square roots using the perfect square method.  The first part is used to generate the multiplication property of square roots and the second part are practice problems.  It can be used to differentiate instruction because the last few problems extend the concept even further.

- Basic Simplifying Square Roots - A basic worksheet designed for practicing the skill of simplifying square roots. 

Topic Discussion

    There are two separate approaches to teaching students how to simplify square roots.  I will discuss both of them, but I think one is more appropriate in an Algebra 1 classroom.  The two methods are The Perfect Square Method and The Prime Factorization Method.  Here is a short description of each method.

The Perfect Square Method – This method is done by factoring the radicand (the number inside the square root) into perfect squares.  Then the square root of the perfect squares are evaluated and the results are multiplied together.

The Prime Factorization Method – This method is done by factoring the radicand into its prime factorization.  The prime factorization is written in exponent form (i.e. ) and then the power is divided in half and placed outside the square root.    There are other ways this is taught, which will be covered later, but all are in essence the prime factorization method. 

    Thus we have to decide which method to teach our students.  In my opinion the answer is both.  I believe very strongly the best way to introduce square roots is the Perfect Square Method.  This is because it provides the students with the best understanding of what it means to simplify square roots.  In combination with the Multiplication Property of Square Roots it is very easy for the students to see what they are doing.  However, the perfect square method has its draw backs.  Most notably it doesn’t translate as well to simplifying square roots that have variables in it.  Thus it becomes important to eventually introduce the idea of dividing the power in half.  It is possible to teach the students to use the perfect square method (i.e..  However, this tends to be more confusing than just remembering that you divide the exponent by two(though essentially they are the same).