Lesson 1

Lesson 1 Summary

In this lesson you investigated the following questions:

• How do you convert between a mixed radical with a numerical radicand and an entire radical?

• Why are radicals expressed in different ways?

You refreshed your knowledge of how to express an entire radical as a mixed radical. You used two different methods.

• Method 1:  Factoring out the greatest perfect square

• Method 2: Completely factoring the radicand into prime factors

Both methods worked, so you can choose whichever method suits the problem and your preference.

At the beginning of this lesson you learned that real roots do not exist for negative radicands with even indexes, such as , , and . Real roots do exist, however, for negative radicands with odd indexes, such as , , and . The radical is only defined as a real number if x is greater than or equal to zero.

You also refreshed your knowledge about how to express a mixed radical as an entire radical. You began by expressing the coefficient as a root to the power of the index of the radical.

You checked the accuracy of your conversions by computing the mathematical values of the question and the answer with a calculator, and ensuring they were the same. You used your knowledge of converting between mixed and entire radicals to order sets of radicals from least to greatest.

In the next lesson you will enhance your ability to work with radicals, including adding, subtracting, multiplying, dividing, and simplifying radicals and their components.