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CBSE Class 10 Answered

If p,q are prime positive integers , prove that root p + root q is an irrational number
Asked by manasvi.gopani | 14 Feb, 2018, 12:44: PM
answered-by-expert Expert Answer
begin mathsize 16px style square root of straight p plus square root of straight q space is space rational space...... assume square root of straight p plus square root of straight q equals straight a over straight b square straight p plus straight q plus 2 square root of pq equals open parentheses straight a over straight b close parentheses squared square root of pq equals 1 half open parentheses open parentheses straight a over straight b close parentheses squared minus straight p minus straight q close parentheses...... left parenthesis 1 right parenthesis now space straight p space and space straight q space are space prime space positive space numbers space so square root of straight p space and space square root of straight q space is space irrational also space square root of pq so space in space left parenthesis 1 right parenthesis irrational space equals space rational so space contradiction end style
Answered by Arun | 14 Feb, 2018, 02:27: PM

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