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Prove that root 7 is a …

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Prove that root 7 is a irrational number

Posted by Sunena Dutta 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Priya ✧*｡٩(๑˙╰╯˙๑)و✧*｡ 5 years, 1 month ago

let us assume that √7 be rational. then it must in the form of p / q. As definition of rational number says.. P is whole number q is non zero whole number.. And p and q is simplest ratio which is expressed.. That means there exists no prime factor common in p and q. √7 = p / q √7 x q = p squaring on both sides 7q² = p² ------1. p is divisible by 7 p = 7c [c is a positive integer] [squaring on both sides ] p²= 49c² subsitute p² in eqn(1) we get 7q² = 49 c² q² = 7c² q is divisble by 7 thus q and p have a common factor 7. there is a contradiction to our assumption as our assumsion p & q are co prime but it has a common factor. so that √7 is an irrational.

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