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CBSE Class 10 Answered

Prove that 2 root 3 divided by 5 is irrational  
Asked by anirudhbanga2017 | 18 Feb, 2018, 08:27: AM
answered-by-expert Expert Answer
begin mathsize 16px style let space fraction numerator 2 square root of 3 over denominator 5 end fraction be space rational fraction numerator begin display style 2 square root of 3 end style over denominator begin display style 5 end style end fraction equals straight p over straight q...... straight p space and space straight q space are space co space prime square 12 over 25 equals fraction numerator begin display style straight p squared end style over denominator begin display style straight q squared end style end fraction straight p squared equals fraction numerator begin display style 12 end style over denominator begin display style 25 end style end fraction straight q squared straight p squared equals straight c space cross times space straight q squared so space straight c space divides space straight p squared ie. space straight c space divides space straight p straight p equals straight c cross times straight k....... say fraction numerator begin display style 2 square root of 3 end style over denominator begin display style 5 end style end fraction equals straight p over straight q straight q equals fraction numerator begin display style 5 end style over denominator begin display style 2 square root of 3 end style end fraction cross times straight p straight q equals fraction numerator begin display style 5 end style over denominator begin display style 2 square root of 3 end style end fraction cross times straight c cross times straight k straight q equals space straight t space cross times space straight c......... straight c space divides space straight q now space straight c space divides space both space straight p space and space straight q space so space contradiction space since space they space are space co space prime so space our space assumption space is space wrong end style
Answered by Arun | 18 Feb, 2018, 03:27: PM

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