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

2. 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

3. 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.

4. 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.

5. 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

6. Rationalize the Denominator
This is a process used to eliminate a radical from the denominator.
Multiply the numerator and the denominator by the radical shown in the denominator.
Simplify.
The idea is to create a square for the denominator so you can get rid of the radical.

7. To simplify expressions with radicals in the denominator, you may be able to rewrite the denominator as a rational number without changing the value of the expression.
The denominator is represented by a quantity. You can not take part of the quantity and undo the radical. You must work with the entire quantity.
Multiply the denominator by its conjugate to create a sum and difference pattern.

8. a2 – b2 The Sum and Difference Pattern a2 – ab + ab – b2
The SUM of a and b
times the DIFFERENCE of a and b.
a2 – ab + ab – b2
After FOIL, the middle terms cancel because they’re opposites.
The result is the difference of the squares of the two original terms.
a2 – b2

9. To simplify expressions with radicals in the denominator, you may be able to rewrite the denominator as a rational number without changing the value of the expression.
Multiply the denominator by its conjugate to create a sum and difference pattern.

10. Do not distribute the numerator until the denominator is simplified!
Another example - Simplify.
Multiply by the conjugate of the denominator to create a sum and difference pattern.
Do not distribute the numerator until the denominator is simplified!

11. Simplify.
Example 1
Example 2
Example 4
Example 3

12. Do not distribute the numerator until the denominator is simplified!
Simplify.
Example 1
Example 2
Distribute.
Do not distribute the numerator until the denominator is simplified!

13. Simplify.
Example 4
Example 3

14. Simplify.

15. Simplify.

16. Simplify.

17. Homework
10-A4 Pages #29–40,71-76