Lesson 4

Lesson 4 Summary

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In this lesson you investigated the following questions:

• How do you determine the roots of a radical equation algebraically?
  
  
• How do you verify that the values determined in solving a radical equation are viable roots of the equation?

You learned how to solve different kinds of equations with variable radicands, including some equations for determining the expected length of skid marks based on the initial speed of the vehicle.

You learned that some radical equations are best solved by isolating the radical and squaring both sides. If there were more than one radical and they could not be combined, you learned to isolate the most complex radical and then square both sides.

Squaring both sides sometimes introduces an extraneous root. The only way to be sure which roots are real is to substitute the roots into the original equation, one at a time. If both the left and right sides of the equation are equal, the root is a real solution to the equation. The root is extraneous if both sides are not equal when the root is substituted in.

Not all numbers can be used for variables in a radical equation. If the radicand is in the denominator, the value of the radicand cannot allow the denominator to equal zero. Also, if the index is an even number, the radicand must not have a negative value.

In the next lesson you will model situations using radical equations.