<prompt> Ikiwa nambari frac12 leftfrac5sqrt33 sqrt32 frac1sqrt3 3 -sqrt32kuliainaweza kuonyeshwa kwa namna sqrt3a sqrt3b, ambapo a na b ni nambari kamili, hesabu ab.  <response>: Tunasawazisha kila sehemu katika mabano, kwa kutumia jumla na tofauti ya vitambulisho vya cubes. Kwanza, tuna beginaligned frac5sqrt33 sqrt32 frac5leftsqrt3 9 - sqrt36 sqrt34kulialeftsqrt33 sqrt32kuliakushoto sqrt39 - sqrt36 sqrt34kulia frac5leftsqrt39 -sqrt36sqrt34kulia32 sqrt39 - sqrt36 sqrt34. endalignedVile vile, anzaaligned frac1sqrt33 - sqrt32 fracsqrt3 9 sqrt36 sqrt34leftsqrt33 - sqrt32kulialeft sqrt39 sqrt36 sqrt34kulia fracsqrt39sqrt3 6sqrt343 - 2 sqrt39 sqrt36 sqrt34. endalignedKwa hivyo,anzaaligned frac12 leftfrac5sqrt33 sqrt32 frac1sqrt33 -sqrt32kulia frac12 kushotoleftsqrt39 -sqrt36sqrt34kulia kushotosqrt39sqrt36sqrt34 kulia kulia sqrt39 sqrt34, mwishoiliyopangwahivyo ab9413. 