<prompt> Rahisisha usemi sqrt37-20sqrt3.  <response>: Tunatafuta nambari kamili a na b kiasi kwamba sqrt37-20sqrt3 a-bsqrt3.Kuweka pande zote mbili, tuna 37-20sqrt3a-bsqrt32 a23b2 - 2absqrt3. Kwa hiyo, ni lazima tuwe na tuanzeiliyolingana a23b2 37, -2ab -20. endiliyolinganaMlinganyo wa pili unatoa ab10. Tukijaribu jozi za kipengele cha 10, tunapata kuwa a,b5,2 inatosheleza a23b2 37. Kwa hiyo, 37-20sqrt35-2sqrt32. Kwa kuwa 5-2sqrt3 ge 0, inafuata kwamba sqrt37-20sqrt3 5-2sqrt3. 