The document discusses different ways of writing radicals and rational exponents. It explains that radicals can be written as rational exponents, which may make problems easier to solve. The document also emphasizes that radicals should never be left in denominators, and fractions with radical denominators should always be rationalized by multiplying the numerator and denominator by the denominator's conjugate.

1. RADICALS radicand index The nth root of a number k is a number r which, when raised to the power of n , equals k r

2. RADICALS r So, means that r n =k

3. Rational exponents We usually express roots this way! Rational exponent

4. Rational exponents So, these three ways to express roots are equivalent! Notice that when you are dealing with a radical expression, you can convert it to an expression containing a rational (fractional) power. This conversion may make the problem easier to solve .

5. Properties of Radicals Why? Why? Why? Why? Why? AHEAD

6. Properties of Radicals BACK AHEAD

7. Properties of Radicals BACK AHEAD

8. Properties of Radicals BACK AHEAD

9. Properties of Radicals BACK AHEAD

10. Properties of Radicals BACK AHEAD

11. Rationalizing Denominators with Radicals You should never leave a radical in the denominator of a fraction. Always rationalize the denominator. Example 1 (monomial denominator) Rationalize the following expression: Answer: AHEAD

12. Rationalizing Denominators with Radicals You should never leave a radical in the denominator of a fraction. Always rationalize the denominator. Example 2 (monomial denominator) Rationalize the following expression: Answer: AHEAD

13. Rationalizing Denominators with Radicals You should never leave a radical in the denominator of a fraction. Always rationalize the denominator. Example 3 (binomial denominator) Rationalize the following expression: Answer: You will need to multiply the numerator and denominator by the denominator's conjugate AHEAD

14. Exercises Now, you can practice doing exercises on your own… THE MORE YOU PRACTICE, THE MORE YOU LEARN … and remember…