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MATHIO4 Hw | (a) Proves YS ivvational Proof by cwoaladiction: Assume 3 is rational —> f7 €Q - fee - p.7 eZ, 440 pia aie akin factor Pe a -™d £. L if x Aviles £ ad x divides & 2 1 thn x =| ‘ ee =: et > spp 3 divides p* 9 3 divides p< 34 aed (hy Fran ol : sl, ree 34° = 4a — 4 23a" ~~ 3 nas 4 Thin of Av IHede) 3 ites 4 also “TE 4 dividus ? awa 3 divides q) Pec G L hove & Common factor of 3 — CONTKADICTLION Sam the statement thot r and Y donee Kanes: common fartor® 3 is ircational. Yes, a similar agument worls to show AG is irrational. also Tuskeod of Sayi “g Aivisible by c a 6 lor evn Zor 2 sine thy are both factors of 6), Ne could ceplae 3 wath &. Sal contradiction. b) & weational poof : Assuoe v4 roronal 2 wh < vhs 4 do avt hove common e° t ane 4° ze ~ Hy *f > 4 dvds ¢° (2 LAivils P > 2 divide p v 4q*e (2m) ‘ean 2 4ten ape £24 pein neZ Ne. contradiction because 4 do not have common factors whan qstl (pee?) Ladd act eglativaly prime . - NG is cational Thire 1S ont instant White a % £ Ard PY ke not haut tommy factoy, so it is rational. 
