1. SIMPLIFYING RADICAL EXPRESSIONS
A RADICAL EXPRESSION is an expression that contains a square root.
Examples: or
The RADICAND is the expression under the radical sign.
For , the radicand is 5ab3

2. SIMPLIFYING RADICAL EXPRESSIONS
A radical expression is in SIMPLEST FORM if it contains no perfect square factors other than 1.
Examples:
is in simplest form.
is NOT in simplest form. Why?

3. FLASH CARDS
Simplified or Not?
YES! J

4. FLASH CARDS
Simplified or Not?
NO!
4 is a factor! L

5. FLASH CARDS
Simplified or Not?
NO!
x2 is a factor! L

6. FLASH CARDS
Simplified or Not?
NO!
9x2 is a factor! L

7. FLASH CARDS
Simplified or Not?
YES! J

8. SIMPLIFYING RADICAL EXPRESSIONS PRODUCT PROPERTY OF SQUARE ROOTS

9. SIMPLIFYING RADICAL EXPRESSIONS
SIMPLIFYING RADICALS

10. SIMPLIFYING RADICAL EXPRESSIONS
SIMPLIFYING RADICALS
NOTICE THAT ONLY THE POSITIVE SQUARE ROOT IS USED.

11. FLASH CARDS
Simplify J

12. FLASH CARDS
Simplify J

13. FLASH CARDS
Simplify J

14. FLASH CARDS
Simplify J

15. FLASH CARDS
Simplify J

16. FLASH CARDS
Simplify J

17. SIMPLIFYING RADICAL EXPRESSIONS
are examples of irrational numbers.
Simplified expressions can not have irrational numbers (square roots) in their denominators.
RATIONALIZING THE DENOMINATOR is a method used to eliminate radicals from the denominator of a fraction.

18. SIMPLIFYING RADICAL EXPRESSIONS
Step 1:
Multiply numerator & denominator by the radical in the denominator.
Step 2:
Simplify, Reduce

19. SIMPLIFYING RADICAL EXPRESSIONS
Step 1:
Multiply numerator & denominator by the radical in the denominator.

20. SIMPLIFYING RADICAL EXPRESSIONS
Can we just divide?
Simplify:
YES!
Step 1:
Multiply numerator & denominator by the radical in the denominator.
Step 2:
Simplify, Reduce

21. SIMPLIFYING RADICAL EXPRESSIONS
If the denominator is a binomial with a radical, i.e.
Then multiply the numerator and denominator by the CONJUGATE of the denominator.
The conjugate of is
The conjugate of is

22. SIMPLIFYING RADICAL EXPRESSIONS
Step 1:
Multiply numerator & denominator by the conjugate of the denominator.
Step 2:
Simplify, Reduce

23. SIMPLIFYING RADICAL EXPRESSIONS
Try this one:
Step 1:
Multiply numerator & denominator by the conjugate of the denominator.
Step 2:
Simplify, Reduce

24. SIMPLIFYING RADICAL EXPRESSIONS
Try this one:
Step 1:
Multiply numerator & denominator by the conjugate of the denominator.
Step 2:
Simplify, Reduce

25. SIMPLIFYING RADICAL EXPRESSIONS
Try this one: