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10.5 - 10.5Rationalizing Numerators and Denominators of...

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Unformatted text preview: 10.5Rationalizing Numerators and Denominators of Radical Expressions Many times it is helpful to rewrite a radical quotient with the radical confined to ONLY the numerator. If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator. This process involves multiplying the quotient by a form of 1 that will eliminate the radical in the denominator. Rationalize the denominator. ﬁ(% W vabU/vhli 51:1— 5“, ' ﬂit; 3‘31 J? ...—« "-— 73” W" 33" ,..—— 1. _6_ ii) {/575— V9— 243" ______r 3 W raj; 3 aﬁ- w? + SUE-IE an: u 3er f... ,__. ,_ a 3J9 mm mm M w «(3); (6(3) +3Jﬁj+wﬂ+é 3“? +313 *f Iafz +6 463+! @145 1}? . Ja — b (1)3711}; ) (jumarmlov 6+, #— f ehamino— Jo? . 332%? {bi (m‘ﬂﬂagiﬁ gm +J/r— dadb +SU/QNE (g‘JZJQ—Uh L) 415+ (if; +\E; 4 6) {£1 Q ~— 5 D, L aa+ﬁb + (11341]? 46L vb ROCHO'YDLB é... ‘4 [’19 d/QIHDTYI [‘OQ‘ILO ‘Y‘ K Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical. The conjugate uses the same terms, but the opposite operation (+ or u). Rationalize the denominator: f+2 ﬁ‘d?) fwl-J— ﬁﬂdg Um) : J4; d3+31f5 fag W @2192; (E); _. [a 2+2f-aatla) l fl g I—g— ad 2_ + E An expression rewritten with no radica in the numerator IS called rationalizing the numerator Rationalize the numerator: 13-— 131... *1 [Q I. V F 13:? 3 314F131 j r________,_,_. W w «Eh/— .— NY ﬁ;§ nﬁigﬂL {X 4'3 @«hﬁﬂ «(r-53) UHB) [pr milik JR )iﬂ’f ' LAMNUA‘D xraJig+j / XHH / ®@> 1X5 JXﬂ +‘ﬂ >< “—ng +3 ...
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