prove that 1/root 7 is an irrational number

Asked by dangerdolane | 8th Apr, 2019, 08:24: PM

Expert Answer:

begin mathsize 16px style Let space us space assume space that space fraction numerator 1 over denominator square root of 7 end fraction space be space straight a space rational space number.
rightwards double arrow fraction numerator 1 over denominator square root of 7 end fraction equals space straight a over straight b space space space left parenthesis where space space straight a space and space straight b space are space co minus prime space and space straight b space not equal to space 0 space right parenthesis
rightwards double arrow square root of 7 space equals space straight b over straight a
We space know space that space square root of 7 space is space an space irrational space space number space but space straight b over straight a space is space space straight a space rational space number.

rightwards double arrow our space assumption space was space wrong.
rightwards double arrow fraction numerator 1 over denominator square root of 7 end fraction space is space an space irrational space space number.



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Answered by Yasmeen Khan | 9th Apr, 2019, 09:52: AM

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