Lesson 1

Try This 4

 

There may be times when you want to change a mixed radical to an entire radical. The same rules of exponents and roots apply.

 

For example, change the mixed radical into an entire radical.

1. Write the coefficient under the radical sign with the index as its exponent. Answer
   
   
2. Arrange for all factors to have an exponent of 1. Answer
   
   
3. Simplify to write the expression as an entire radical. Answer
   
   
4. Use your calculator to verify that the result is equal to . Answer

The same procedure is used for cube roots. For example, change the mixed radical into an entire radical.

5. Write the coefficient under the radical sign with the index as its exponent. Answer
   
   
6. Arrange for all factors to have an exponent of 1. Answer
   
   
7. Simplify to write the expression as an entire radical. Answer
   
   
8. Use your calculator to verify that the result is equal to . Answer

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Example

 

Change to an equivalent entire radical.

 

Begin by expressing the coefficient as a square root because the radical is a square root.

 

 

Check by computing the values for the original question and the answer using a calculator.