Module 4: Dividing Radical Expressions
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1 Her MTH 9 Secio IV: Rdicl Epressios, Equios, d Fucios Module 4: Dividig Rdicl Epressios Recll he propery of epoes h ses h oi logous propery for rdicls:. We c use his propery o (usig he propery of epoes give ove) Quoie Rule for Rdicls If d re posiive rel uers d s posiive ieger, he. EXAMPLE: Perfor he idiced divisio, d siplify copleely (quoie rule for rdicls)
2 (quoie rule for rdicls) ( 4) 4 (Fro ow o we will ssue h vriles uder rdicl sigs represe o-egive uers d oi solue vlue rs.) Quoie Rule for Siplifyig Rdicl Epressios: Whe siplifyig rdicl epressio i is ofe ecessry o use he followig equio which is equivle o he quoie rule:. EXAMPLE: Siplify he followig epressios copleely (quoie rule for siplifyig rdicls) (siplify he rdils i he ueror d deoior) (quoie rule for siplifyig rdicls) ( ) (siplify rdicls i ueror d deoior)
3 EXAMPLE: Perfor he followig divisio:. SOLUTION: The key sep whe he idices of he rdicl re differe is o wrie he epressios wih riol epoes. 1 1 (wrie wih riol epoes) 1 1 (use propery of epoes) (cree coo deoior for he epoe) (wrie fil swer i rdicl oio o gree wih origil epressio) EXAMPLE: Perfor he idiced divisio, d siplify copleely (wrie wih riol epoes) (use propery of epoes) (cree coo deoior for he epoe) (wrie fil swer i rdicl oio o gree wih origil epressio)
4 4. ( ) ( ) 1 1 (wrie wih riol epoes) (use propery of epoes) 1 4 (use oher propery of epoes) (cree coo deoior for he epoes) ( ) (use oher propery of epoes) (wrie fil swer i rdicl oio o gree wih he origil epressio) RATIONALIZING DENOMINATORS [Recll fro Secio I: Module h he se of riol uers cosiss of ll uers h c e epressed s he rio of iegers. I oher words, riol uer c e epressed s frcio where he ueror d deoior re oh whole uers. Alhough i's rue h here re y, y differe frcios ( 1,, 1, 9, ec.), here re y, y, 7 4 y ore uers h co e epressed s frcios. Nuers h co e epressed s rio of iegers re clled irriol uers. (You y e filir wih oe of he chrcerisics of irriol uers: heir decil epsios ever ed d ever repe.) The uer π is proly he os fous irriol uer, u here re los of ohers cully, here re ifiiely y! Mos rdicl epresses re irriol uers, e.g., uers like,,, 1, 4 1, d 7 4 re irriol.] Before he 1970 s here were o elecroic hdheld clculors so heicis, scieiss, d sudes of heics eeded o cosul previously creed les o oi pproiios of clculios. I order o iiize he uer of les h were eeded, ll clculios were de y usig uers whose deoiors were riol uers. Thus, i he "old-dys", i ws ipor o e le o riolize deoiors. so you could he look le d ge pproiio. Bu s he Collecor's Guide o Pocke Clculors ses, 1971 herlded he ge of he low-cos cosuer hdheld clculor. Nowdys, we ll hve clculors h c redily give us highly ccure pproiios of clculios. Alhough we o loger eed o riolize deoiors i order o oi pproiios of clculios, he skill we ler i his secio is ipor lgeric ipulio used i clculus d eyod. Sice rdicl epressios re ofe irriol, we sudy riolizig deoiors while we re focusig o rdicl epressios. I his coe, riolizig deoiors cosiss of geig ll of he rdicls ou of he deoior of he epressio.
5 EXAMPLE: Riolize he deoiors i he followig epressios:.. 8 c.. (oi perfec squre uder he squre roo i he deoior) (oi perfec cue uder he cue roo i he deoior) c. (oi power-of-five uder he fifh roo i he deoior)
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