5.6 - Reteach Radical Epressios ad Ratioal Epoets Use Properties of th Roots to siplify radical epressios. Product Property: ab a b Siplify: 8 8. Factor ito perfect fourth roots. Use the Product Property. Thik: a a, so ad. Quotiet Property: Siplify: 9. a b a b Always ratioalize the deoiator whe a epressio cotais a radical i the deoiator. 9 Use the Quotiet Property. Siplify the uerator. Thik: Ratioalize the deoiator. Use the Product Property. Siplify. 9. Siplify each epressio. 8.. 8 6. 6 5 8 8 6 6. 5 0 5. 6. 8 65 Origial cotet Copyright by Holt McDougal. Additios ad chages to the origial cotet are the resposibility of the istructor. Holt McDougal Algebra
5.6 - Reteach Radical Epressios ad Ratioal Epoets (cotiued) The th root of a uber ca be represeted usig a ratioal, or fractioal, epoet: a a. Eaples: 6 6 6 56 56 This eas to take the th root of a. Powers ad roots ca be epressed usig ratioal epoets a a. Eaples: 6 6 6 5 5 6 To write epressios usig ratioal epoets, use the defiitios. The deoiator is the root ad the uerator is the power. a a ad a a Eaples: 5 5 6 6 Note that a a. Thik: The root is. The power is. Write each epressio i radical for ad siplify. 7. 7 7 8. 9 9. 6 Write each epressio by usig ratioal epoets. 0. 5 Thik:, 5. 9. 5 6 Siplify each epressio... 9 8 6 5. 7 Origial cotet Copyright by Holt McDougal. Additios ad chages to the origial cotet are the resposibility of the istructor. Holt McDougal Algebra
5-7 Reteach Radical Fuctios The square root fuctio, f The doai of f is { 0}. The rage is {y y 0}., is a radical fuctio. You ca ake a table of values to graph a radical fuctio. Graph: f Note that ad y have oly oegative values. f (, f()) f 0 0, 0) f, ) f (, ) 6 f 6 6 9 (6, ) First choose the value of that akes f() 0. First choose the value of that akes perfect squares. The doai is { }. The rage is {y y 0}. Graph the fuctio. Idetify its doai ad rage.. f f (, f()) Doai: Rage: Origial cotet Copyright by Holt McDougal. Additios ad chages to the origial cotet are the resposibility of the istructor. Holt McDougal Algebra
5-7 Reteach Radical Fuctios (cotiued) Trasforatios of the square root fuctio, f(), are siilar to trasforatios of other fuctios. Trasforatios Vertical Traslatios y k Shifts f() up k uits for k 0 Shifts f() dow k uits for k 0 k, so g( ) shifts f() uit dow. Horizotal Traslatios y h Shifts f() right h uits for h 0 Shifts f() left h uits for h 0 h, so ( ) shifts f() uits left. Reflectios y reflects f() across -ais y reflects f() across y-ais r( ) reflects f() across the y-ais. Usig the graph of f ( ) as a guide, describe the trasforatio ad graph each fuctio.. s( ). p( ) k : Origial cotet Copyright by Holt McDougal. Additios ad chages to the origial cotet are the resposibility of the istructor. Holt McDougal Algebra
5-8: Reteach Solvig Radical Equatios ad Iequalities Solve radical equatios by raisig both sides of the equatio to the power of the ide of the radical. For eaple, the ide of a is. Therefore, 9 Solve: 8 Step Step Step Step 5 Isolate the radical. Divide both sides of the equatio by ad siplify. 8 6 Square both sides of the equatio ad siplify. 6 Solve. 8 6 Check. 8 8 6 6 8 Solve each equatio. Check your aswer... 5 9. 0 5 5 9 5 The ide of is. Raise both sides to the power of. Reeber: a a. Always check for etraeous solutios whe solvig radical equatios. Origial cotet Copyright by Holt McDougal. Additios ad chages to the origial cotet are the resposibility of the istructor. Holt McDougal Algebra
5-8: Reteach Solvig Radical Equatios ad Iequalities (cotiued) Solvig equatios with ratioal epoets is siilar to solvig radical equatios. Solve: 0 Step Step Step Step Step 5 Step 6. Raise both sides to the reciprocal power. 0 Square both sides. 0 Write the quadratic equatio i stadard for. 0 0 Factor. ( ) ( 5) 0 Solve. ( ) 0 or ( 5) 0 5 Check for etraeous solutios. 0 5? 0 5? 5 0 6 5 5 The reciprocal of Set oe side of the equatio equal to zero. Thik: a a This is the oly solutio. is. Solve each equatio.. 5 6 5. 6 8 6. 6 5 6 Origial cotet Copyright by Holt McDougal. Additios ad chages to the origial cotet are the resposibility of the istructor. Holt McDougal Algebra