1. Math 20-1 Chapter 5 Radical Expressions and Equations 5.2 Multiply and Divide Radicals Teacher Notes

2. Notice the coefficients are multiplied and the variables are multiplied. x must be a number greater or equal to zero.

3. 5.2 Multiply and Divide Radical Expressions When multiplying radicals, multiply the coefficients and multiply the radicands. The indices must be the same. Product Property Note Domain: When k is even a ≥ 0 and b ≥ 0. = ( ) coefficient x coefficientradicand x radicand 5.2.1

4. Multiply Radicals Multiply. Simplify where possible. To multiply a polynomial by a monomial, use the distributive property to remove parentheses and then simplify each resulting term, if possible. 5.2.2

5. Multiply Radicals Your Turn Multiply. Simplify where possible 5.2.3

6. Quotient Rule with Radicals When dividing radicals, divide the coefficients and then divide the radicands. You can only divide radicals with the same index. Divide and simplify. 5.2.4

7. To rationalize the denominator, multiply both numerator and denominator by the radical that will cause the denominator to become a rational number. Rationalizing the Denominator Simplify For an expression with a monomial square root denominator, multiply the numerator and denominator by the radical term from the denominator 5.2.5 Rationalize the denominator:

8. Rationalize and, if possible, simplify. Rationalizing Binomial Denominators To rationalize a denominator that contains a binomial expression involving square roots, multiply its numerator and denominator by the conjugate of its denominator. Conjugate binomials are binomials with the same terms but with opposite signs between their terms 5.2.6

9. Suggested Questions: Page 289: 1b,c, 2a,c,d, 4a,b,e, 5d, 6, 8a,c,d, 9a,c, 10, 13, 15, 25