1. Operations with Radical Expressions √
Algebra
Operations with Radical Expressions √

2. Review: Simplifying √ Expressions
Prime factorization can be useful
1. Factor terms under the radical.
Find the largest perfect square factor(s).
Take square roots outside.
2. Rewrite in simplified form.

3. Warm-Up: You try.

4. Adding and Subtracting Radicals
You can add and subtract terms that have the same radicand and index.
These are LIKE TERMS.

5. Add and Subtract: You try.
Simplify each radical term first

6. Add and Subtract: Simplify each term first.

7. Multiplying Radicals 1. Multiply terms outside the radical together.
2. Multiply terms inside the radical together.
3. Simplify.

8. Multiplying Radicals
You can multiply using distributive property and FOIL.
It’s a DTS!

9. Multiply: You try.
It’s a PST!

10. Dividing to Simplify Radicals
No radicals in the denominator allowed
Denominators must be “rationalized.” √
Multiply by 1in the form of √ 3 1

11. Using the Conjugate to Simplify
The other part of a DTS
Expression
Conjugate
Product
The radical “goes away” every time

12. Dividing to Simplify Radicals
conjugate
Multiply by 1in the form of
conjugate 5 1 11

13. Simplify: You try.

14. Summary: To ADD and SUBTRACT To MULTIPLY To DIVIDE COMBINE LIKE TERMS
“Outside” NUMBERS x NUMBERS
“Inside” NUMBERS x NUMBERS
DISTRIBUTE and FOIL
To DIVIDE
“Rationalize” denominator using 1
Use conjugate
ALWAYS SIMPLIFY AT THE END IF YOU CAN

15. Homework