1. You should know or start to recognize these: 2 2 = 43 2 = 94 2 = 165 2 = 25 2 3 = 83 3 = 274 3 = 645 3 = 125 2 4 = 163 4 = 814 4 = 2565 4 = 625 2 5 = 323 5 = 2434 5 = 1024 5 5 = 3125

2. Chapter 7 Section 1 Roots and Radical Expressions

3.  5 2 = 255 is a square root of 25  Since 5 2 = 255 is a square root of 25  5 3 = 1255 is a cube root of 125  Since 5 3 = 1255 is a cube root of 125  5 4 = 6255 is a fourth root of 625  Since 5 4 = 6255 is a fourth root of 625  5 5 = 31255 is a fifth root of 3125  Since 5 5 = 31255 is a fifth root of 3125

4. **Roots and Exponents are inverse operations**  For any real numbers a and b, and any positive integer n, if a n = b then a is the n th root of b.  Note: We are now working in REAL numbers only. (This means we will not be using i for any of our answers)

5. If the root is even then there can be two answers is the principal root which indicates a positive answer is the other root which indicates a negative answer index radicand radical sign  If the root is odd then there can be only one answer (the same sign as the radicand)

6. Find each real-numbered root

7. Simplify these Radical Expressions

10. Simplifying Radical Expressions  Hint: –Divide the exponent by the index, write how many times it goes in evenly and what is left over  Absolute Value symbols are needed when you have an even root that results in an odd exponent (see previous examples)