1.1 Radical Expressions Rationalizing Denominators

1 Calculus and Vectors How to get an A+ Radical Expressions : Rationalizing Denominators - Handout 2010 Iulia & Teodoru Gugoiu - Page 1 of 2 Radical Expressions : Rationalizing Denominators - Handout A Radicals mnnmnmnnaaaaaaaa)()()(==== Note: If n is even, then 0 a for na. Ex 1. Simplify: a) 33 b) 3)5( c) 53)7( B Rationalizing Denominators (I) bccacccbacba== Ex 2. Rationalize: 532 C Conjugate Radicals dcbadcbacbacbababababa + + + + Ex 3. For each expression , find the conjugate Radical . a) +32 b) 32 c) +523 d) +7352 D Difference of squares identity 22))((bababa = + Ex 4.

2 Use the difference of squares identity to simplify: a) ))((baba + b) ))((baba + c) ))((cbacba + E Rationalizing Denominators (II) Hint: Multiply and divide by the conjugate Radical of the denominator. Ex 5. Rationalize the denominator: a) 213 b) 5324+ c) 632 F Rationalizing Numerators Hint: Multiply and divide by the conjugate Radical of the numerator. Ex 6. Rationalize the numerator: 1235 G Equivalent Expressions Hint: You may get equivalent Expressions by Rationalizing the numerator or denominator. Note: State restrictions.

3 Ex 7. Find equivalent Expressions by Rationalizing . State restrictions. a) 11 xx b) xx39 + Calculus and Vectors How to get an A+ Radical Expressions : Rationalizing Denominators - Handout 2010 Iulia & Teodoru Gugoiu - Page 2 of 2 c) hxhx11 + H More algebraic identities ))()(())(())((224422332233bababababababa bababababa++ = + +=+++ = Ex 8. For each case, the numerator and denominator have a common zero. Use algebraic identities to eliminate the common zero. State restrictions. a) 113 xx b) 1134 xx Reading: Nelson Textbook, Pages 6-8 Homework: Nelson Textbook: Page 9, #1a, 2a, 3a, 4a, 5, 6a, 7ac