Lesson 1

Explore

If you recognize that a perfect square is a factor of your radicand, you can simply write the radicand as the product of the perfect square and another number and then simplify.

Self-Check 1

Consider the radical .

1. Write the radicand as a product of two factors, one of which is a perfect square. Answer
   
   
2. Simplify the result by evaluating the square root of the perfect square. (Hint: is the perfect square.) Answer
   
   
3. Write the expression as a mixed radical. Answer
   
   
4. Use your calculator to verify that the result is equal to . Answer
   
   
5. What other ways could you simplify ? Answer

Self-Check 2

Change the following entire radicals into equivalent mixed radicals using one method; then check your answers using the other method. Which method works better for you? Be sure to check your answers to ensure that you understand the solution process.

1. Answer
   
   
2. Answer
   
   
3. Answer
   
   
4. Answer