1. 10-1A Simplifying Radicals
Algebra Glencoe McGraw-Hill Linda Stamper

3. You have simplified fractions.
answer

4. All radical answers must be in simplified form!
Simplifying Radicals
The simplest form of a radical expression is an expression that has:
No perfect square factors other than 1 in the radicand.
not simplified
No fractions in the radicand.
not simplified
No radicals in the denominator of a fraction.
not simplified
All radical answers must be in simplified form!
Use the properties of radicals to simplify radical expressions.

5. Product Property of Radicals
Rewrite using a perfect square factor.
Write each factor as a radical.
Simplify.
An efficient method is to find the largest perfect square factor.

6. Simplify.
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6

7. Simplify.
Example 1
Example 2
Example 3
Why isn’t the answer
Because the problem was not

8. Simplify.
Example 4
Example 5
Example 6

9. Product Property of Radicals
Rewrite using a perfect square factor.
Write each factor as a radical.
Simplify.
Multiply radicals using the product property.
Rewrite as one radical.
Simplify.

10. Simplify.
Example 7
Example 8
Example 9

11. Simplify a square root with variables.
When finding the principal square root of an expression containing variables, be sure that the result is not negative.
It may seem that the answer is… ?
What if x has a value of -2. ?
Substitute -2 for x in the equation.
For radical expressions where the exponent of the variable inside the radical is even and the resulting simplified exponent is odd, you must use absolute value to ensure nonnegative results.

12. Write the radicand as prime factors.
Simplify.
Write the problem.
Write the radicand as prime factors.
Simplify.
Use good form – alphabetical order (inside and outside of the radical) with radical last.
If the power of the variable is an odd number, write the variable with absolute value bars

13. Simplify.
You can have more than one variable in absolute value bars.

14. Simplify.
Example 10
Example 11
Example 12

15. Simplify.
Example 10
Example 11
Example 12

16. Homework
10-A2 Pages #17–28,68-70.