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Prove that √7 be irrational

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Prove that √7 be irrational

Posted by Deepti Kukreja 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Payal Thakur 6 years, 10 months ago

Sry yrr glti se 7 ki jgh 3 ho gya aap 7 kr lena 3 ki jgh baki same ese hi h

Payal Thakur 6 years, 10 months ago

Let us assume to the contrary ,that √3 is rational. That is,we can find integers a and b(#0 )such that√3=a/b. Suppose a and b have a common factor other tha 1,then we can divide by the common factor , and assume that a and b are coprime. So,b√3=a Squaring both sides, a2 is divisible by 3 that a is also divisible by 3 So,we can write a=3c for some integer c. Substituting for a,we get 3b2= 9c2. This means that b2 is divisible by 3,and so b is also divisible by 3 ..a and b have at least 3 as a common factor. But this contradicts the fact that a and b are coprime .. This contradiction has arisen because of our incorrect assumption that √3 is rational.. So,we conclude that √3 is irrational..??

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