Technical Mathematics, Sixth Edition

13.4. Radical Equations

A radical equation is one in which the unknown is under the radical sign.

Example 47: The equation is a radical equation.

▪ Exploration:

Try this. Use your graphing calculator to graph the function

Does the curve cross the x axis? What is the meaning of any such x-intercept? If you substitute it back into the given equation, what do you find?

13.4.1. Approximate Solution of Radical Equations by Graphing

We learned how to find the approximate solution of equations by graphing in Chap. 5. Recall that we moved all terms of the given equation to one side and graphed that expression. Then by zooming in and using or zero we were able to find the value of x at which the curve crossed the x axis to any precision we wanted. That method works for any equation, and we use it here to solve a radical equation.

Example 48: Find an approximate solution to the equation given in Example 47. Solution: Rearranging the equation gives So we graph the function as shown. Using , or zero, we verify that the root is at x = −4.

TI-83/84 screen for Example 48. Graph of , showing ...