Transcription of 1.1 Radical Expressions Rationalizing Denominators
1 calculus and Vectors How to get an A+ Radical Expressions : Rationalizing Denominators 2010 Iulia & Teodoru Gugoiu - Page 1 of 2 Radical Expressions : Rationalizing Denominators A Radicals mnnmnmnnaaaaaaaa)()()(==== Note: If n is even, then 0 a for na. Ex 1. Simplify: a) 333= b) 555)5()5(23== c) 3322323335349777)7(7)7()7()7(==== B Rationalizing Denominators (I) bccacccbacba== Ex 2. Rationalize: 1552535255532532= == C Conjugate Radicals dcbadcbacbacbababababa + + + + Ex 3. For each expression, find the conjugate Radical . a) 3232 + b) 3232+ c) 523523 + d) 73527352 + D Difference of squares identity 22))((bababa = + Ex 4. Use the difference of squares identity to simplify: a) babababa = = +222)())(( b) babababa = = +22)()())(( c) cbacbacbacba222)()())(( = = + E Rationalizing Denominators (II) Hint: Multiply and divide by the conjugate Radical e of the denominator.
2 Ex 5. Rationalize the denominator: a) )21(321)21(3)2(1)21(3212121321322+ = += +=++ = b) 41)532(4594)532(4)53(2)532(4532532532453 2422 = = = +=+ c) 3)63(263)63(2)6()3()63(2636363263222+ = += +=++ = F Rationalizing Numerators Hint: Multiply and divide by the conjugate Radical of the numerator. Ex 6. Rationalize the numerator: )35)(12(2)35)(12()3()5(35351235123522+ =+ =++ = G Equivalent Expressions Hint: You may get equivalent Expressions by Rationalizing the numerator or denominator. Note: State restrictions. Ex 7. Find equivalent Expressions by Rationalizing . State restrictions. a) 1,0,11)1)(1(111111 += + =++ = xxxxxxxxxxxx b) 0,9,391)39(39393939 ++=++=++++ += +xxxxxxxxxxxx calculus and Vectors How to get an A+ Radical Expressions : Rationalizing Denominators 2010 Iulia & Teodoru Gugoiu - Page 2 of 2 c) 0,0,0,11)(1111111 >>+ +++ = ++ += +hxhxxhxhxxxhxhxhxhxhx H More algebraic identities ))()(())(())((224422332233bababababababa bababababa++ = + +=+++ = Ex 8.
3 For each case, the numerator and denominator have a common zero. Use algebraic identities to eliminate the common zero. State restrictions. a) 1,11)1))((1(11)(11332332333333 ++= ++ = = xxxxxxxxxxx b) 1,1)1)(1()1)(1()1)(1)(1(11222234 ++++=++ ++ = xxxxxxxxxxxxx Reading: Nelson Textbook, Pages 6-8 Homework: Nelson Textbook: Page 9, #1a, 2a, 3a, 4a, 5, 6a, 7ac
