<prompt> Nambari sqrt104sqrt6468sqrt10144sqrt152006inaweza kuandikwa kama asqrt2bsqrt3csqrt5, ambapo a , b, na c ni nambari kamili chanya. Tafuta acdot bcdot c.  <response>: Tuna kushotoasqrt2bsqrt3csqrt5kulia2 104sqrt6468sqrt10144sqrt 152006,au 2absqrt62acsqrt102bcsqrt152a23b25c2104sqrt 6468sqrt10144sqrt152006.Kwa kuwa a,b,c ni nambari kamili, tunapata milinganyo minne beginaligned 2ab 104, 2ac 468, 2bc 144, 2a23b25c2 2006. mwishoiliyopangwaHivyo, ab52, ac234 , na bc72. Ili kupata abc, tunazidisha milinganyo hii mitatu pamoja, kupata abc2 52 cdot 234 cdot 72 22 cdot 13 cdot 2 cdot 32 cdot 13 cdot 23 cdot 32 26 cdot 34 cdot 132.Kisha, abc 23 cdot 32 cdot 13 936.Tunaweza kutatua milinganyo ab 52, ac 234, na bc 72 ili kupata a 13, b 4, na c 18, ambayo inatosheleza 2a 2 3b2 5c2 2006. Kwa hivyo, nambari kamili chanya a,b, c zipo. 