1. Simplifying Radicals

2. Simplifying Radicals To simplify a radical
1) Factor the radicand to primes
2) “Each pair is one square”
take each pair from under the radical as one value
3) Multiply any values in front for new coefficient
4) Multiply any values left inside for new radicand

3. Simplifying Radicals
Simplify the following radicals

4. Simplifying Radicals
Simplify the following radicals

5. Simplifying Radicals
Simplify the following radicals

6. Simplify Radicals
Simplify the following radicals

7. Multiplying/Dividing Radicals
Coefficients can multiply/divide and stay outside
Radicands can multiply/divide and stay inside
Simplify as before
Shortcut
Remember

8. Multiply/Divide Radicals

9. Multiply/Divide Radicals

10. Add/Subtract Radicals
In order to add or subtract terms, the radicands must be the same, the rules are just like those for variables, add the coefficients and leave the radicands.
Do not simplify

11. Add/Subtract Radicals
Always remember to see if your terms will simplify before you give up!

12. Add/Subtract Radicals

13. Rationalize a term
To rationalize a term means to clear any radicals from the denominator.
To do that we multiply by a “fancy form of 1” that matches the radical we want to remove from the bottom.
Ex:

14. Rationalizing
Rationalize

15. PRACTICE WS