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Prove root7+root5 is an irrational |
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Answer» first assume that it is rationalise in the form of p/q where p and q are co prime nos.root 5+rot7=p/qwhole square both side...12+2root35=(p/q)whole sqaretherefore root 35=(p square-12q square)/q squarelhs= irrational no.rhs=rational no.this contradicts our assumption that root5+root7 is rational..therefore it is irrational no. Let √7+√5 be rational and its simplest form be a/b where a and b are co primes.Then √7+√5=a/bSquaring on both sides12+2√35=a square/b square2√35=a square /b square -12√35=a square -12b square/2b squareSince the number on the rhs is a non zero integer Therefore it is a rational numberThen √35 is also a rational numberBut this contradicts the fact that √35 is an irrational number Therefore our supposition is wrongHence √7+√5 is an irrational number This* Thai is an ncert ques see in ncert question |
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