1. Simplifying
Radical Expressions

2. When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals.
What is the Product Property of Radicals???

3. Product Property of Radicals
For any real numbers a and b, and any integer n, n>1,
1. If n is even, then
When a and b are both nonnegative.
2. If n is odd, then

4. Let’s do a few problems together.
Factor into squares
Product Property of Radicals

5. Product Property of Radicals
Factor into cubes if possible
Product Property of Radicals

6. Now, you try these examples.

7. Here are the answers:

8. Quotient Property of Radicals0,
For real numbers a and b, b
And any integer n, n>1,
Ex:

9. In general, a radical expression is simplified when:
The radicand contains no fractions.
No radicals appear in the denominator.(Rationalization)
The radicand contains no factors that are nth powers of an integer or polynomial.

10. Simplify each expression.
Rationalize the denominator
Answer

12. To simplify a radical by adding or subtracting you must have like terms.
Like terms are when the powers AND radicand are the same.

13. Here is an example that we will do together.
Rewrite using factors
Combine like terms

14. Try this one on your own.

15. You can add or subtract radicals like monomials
You can add or subtract radicals like monomials. You can also simplify radicals by using the FOIL method of multiplying binomials.
Let us try one.

16. Since there are no like terms, you can not combine.

17. Lets do another one.

18. When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. This gives a rational denominator.

19. Simplify: Multiply by the conjugate. FOIL numerator and denominator.
Next

20. Combine like terms
Try this on your own:

21. Here are a mixed set of problems to do.

22. Answers to the mixed set of problems.