Your answers seem to be incorrect:

Expected:
sqrt(1179090294573338820122431368020571219193838496144981853128507405455819949176596069394854257633924) = 1085859242523329457395988000000000000000000000000
sqrt(85767278828367782602943401434250693589891146724341410177841229729859128397916522826887698538486) = 292860510872271379029706058286700319780600952712

Actual:
1085859242523329457395988099999999999999999999999**2 = 1,179,090,294,573,338,820,122,431,585,192,419,723,859,729,975,339,438,281,514,953,341,085,208,023,800,000,000,000,000,000,000,001
292860510872271379029706058286709999999999999999**2 = 85,767,278,828,367,782,602,943,401,434,256,363,497,888,268,044,527,690,838,818,081,341,940,587,883,426,580,000,000,000,000,001

What language? What are inputs causing your solution to fail?