1. Simplifying Radical Expressions

2. A radical expression is in simplest form if no perfect squares other than 1 are in the radicand, no fractions are in the radicand, and no radicals appear in the denominator of the fraction.

3. Example 1A

4. Example 1B

5. Example 1C

6. Example 1D

7. Example 1E

8. Example 1F

9. Example 1G

10. Example 1H

11. The binomials a + and a - are called radical conjugates.

12. The process of eliminating a radical from an expression’s denominator is called rationalizing the denominator.

13. Example 2A

14. Example 2B

15. Example 2C

16. Example 2D

17. The Product Property of Radicals states that the square root of a product equals the product of the square roots of the factors.

18. Example 3A

19. Example 3B

20. Example 3C

21. Example 3D

22. The Quotient Property of Radicals states that the square root of a quotient equals the quotient of the square roots of the numerator and denominator.

23. Example 4A

24. Example 4B

25. Example 4C

26. Example 4D