<prompt> Pata thamani ya chini yafraca2 b22a3 bkwa nambari halisi chanya a na b. Weka jibu katika fomu iliyorahisishwa fracm sqrtnp, ambapo m, n, na p ni nambari kamili chanya.  <response>: Kupanua, tunapatafraca2 b22a3 b fraca4 2a2 b2 b4a3 b fracab frac2ba fracb3a3.Hebu x fracba, hivyofracab frac2ba fracb3a3 x3 2x frac1x. Na AM-GM,anzaalignx3 2x frac1x x3 fracx3 fracx3 fracx3 frac x3 fracx3 fracx3 frac19x frac19x frac19x frac19x frac19x frac19x frac19x frac19x frac1 9x ge 16 sqrt16x3 cdot kushoto fracx3 kulia6 cdot kushoto frac19x kulia9 16 sqrt16frac1324 frac16 sqrt39.endalignUsawa hutokea wakati x frac1sqrt3, kwa hivyo thamani ya chini ni frac16 sqrt39. 