Square Root Property

The square root property is one method that is used to find the solutions to a quadratic (second degree) equation.  This method involves taking the square roots of both sides of the equation.  Before taking the square root of each side, you must isolate the term that contains the squared variable.  Once this squared-variable term is fully isolated, you will take the square root of both sides and solve for the variable.  We now introduce the possibility of two roots for every square root, one positive and one negative.  Place a  sign in front of the side containing the constant before you take the square root of that side.

Example 1:

     … the squared-variable term is isolated, so we will take the square root of each side

                    … notice the use of the  sign, this will give us both a positive and
                                               a negative root
         … simplify both sides of the equation, here x is isolated so we have
                                               solved this equation 

Example 2:

                  … again the squared-variable term is isolated, so we will take the
                                             square root of each side
         … again don’t forget the  sign, now simplify the radicals

                      … this time p is not fully isolated, also notice that 4 are rational
                                                         numbers, which means …



Example 3:

              … squared term is not isolated, add 1 to each side before beginning

        … now take the square root of both sides

              … simplify radicals

       … radical containing the constant cannot be simplified, solve for the variable

       … notice the placement of the –1 before the radical on the right-hand
                                                         side, these numbers may not be combined since –1 is a rational
                                                         number and  are irrational numbers


In each of the (above) 3 examples involving the square root property, notice that there were no first-degree terms.  These equations although they are quadratic in nature, have the form or

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 15-Nov-2007