Properties of Radical Expressions

1. Properties of Radical Expressions Section 8.2

2. Properties of Radical Expressions • The square root function is a particular case of a larger group of functions called radical functions. This group also includes cube roots ( ) and fourth roots ( ) for instance.

3. Properties of Radical Expressions • We know that iff . • Thus because . • Similarly, iff . • Thus because . • Also iff . • Thus because . • Generally Speaking, iff .

4. Properties of Radical Expressions • Since and , 4,9, 16 are called perfect squares. • (4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169…) • Similarly 8, 27, and 81 would be examples of perfect cubes. • 16, 81, and 256 would be perfect fourths.

5. Properties of Radical Expressions • If you take the square root of a number that is not a perfect square (i.e. ) or the cube root of a number that is not a perfect cube ( ) the resulting value will be an irrational number. • Occasionally you will be asked to approximate the radicals, but MOST TIMES you will just simplify the expressions.

6. Rules for simplifying a radical expression • A square root expression is not simplified if the radicand has a perfect square as a factor. A cube root expression is not simplified if the radicand has a perfect cube as a factor, etc. • A radical expression is not simplified if the radicand is a factor. • A radical expression is not simplified if the radical is in the denominator of the fraction.

7. Rules to simplify radicals • Product Property: • and • Quotient Property: • and • Power Property: • where a ≥ 0 when the index, n, is even.

8. Perfect Squares

9. Perfect Cubes