1. Radicals Simplify, Add, Subtract, Multiply, Divide and Rationalize

2. What is a radical?
It is a symbol placed over a number to indicate the root of a number.

3. Radicals square root cube root fourth root nth root Radical symbol
Index of the radical
Radical symbol
radicand

4. Here are examples of radicals seen before
What type of numbers are 25, 36,49 and 100?

5. Perfect Squares
02 = 0 12 = 1 22 = 4 32 = 9 42 = = = = = = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = = = = = = 625
262 = = = = = 900 …..

6. Simplest Form
A radical expression is in simplest form if the following conditions are true:
No perfect square factors are in the radicand
No fractions are in the radicand
No radicals appear in the denominator of a fraction

7. **Simplifying Radicals**
Find the square root of each number by using the factors (prime factorization!) 81
147 9 9 3 49
Circle the pairs 3 3 3 3 7 7
One number from each pair goes on the outside of the radical (multiplied). All else stays on the inside.
= 3 • 3
= 9

8. **Simplifying Radicals**
Find the square root of each number by using the factors
360 52
525 36 10 2 26 15 35 6 6 2 5 2 13 3 5 5 7 3 3 2 2

9. Multiplying and Dividing Radicals
**Multiplying and Dividing Radicals** Multiply “outside the radical times outside the radical” times “inside the radical times inside the radical”. Same thing with dividing but change the word multiply to divide.

10. Adding and Subtracting Radicals. THEY MUST HAVE THE SAME RADICAL
**Adding and Subtracting Radicals** THEY MUST HAVE THE SAME RADICAL!!!! Sometimes you will have to simplify the radicals first!
Simplify root 8 1st.

11. Rationalizing the Denominator. NO RADICALS IN THE DENOMINATOR
**Rationalizing the Denominator** NO RADICALS IN THE DENOMINATOR!!!! Instead, multiply the numerator and denominator by the radical in the bottom: