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CBSE Class 9 Answered

Prove root 5-root3 is not an rational number
Asked by monisharey20 | 09 Jul, 2019, 09:06: PM
answered-by-expert Expert Answer
Consider, begin mathsize 16px style square root of 5 minus square root of 3 equals straight a over straight b end style
begin mathsize 16px style square root of 5 equals straight a over straight b plus square root of 3 end style
begin mathsize 16px style open parentheses square root of 5 close parentheses squared equals open parentheses straight a over straight b plus square root of 3 close parentheses squared end style
Solving this we get
begin mathsize 16px style square root of 3 equals fraction numerator 2 straight b squared minus straight a squared over denominator 2 ab end fraction end style
√3 is irrational, contradict to the assumption we made.
Hence, given number is not rational.
Answered by Sneha shidid | 10 Jul, 2019, 01:06: PM

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