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Root 7 is irrational

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Root 7 is irrational

Posted by Yash Gaud 4 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Siddhi Bhandari 4 years, 9 months ago

Yogita Ingle 1 year, 7 months ago let us assume that √7 be rational. then it must in the form of p / q [q ≠ 0] [p and q are co-prime] √7 = p / q => √7 x q = p squaring on both sides => 7q2= p2 ------ (1) p2 is divisible by 7 p is divisible by 7 p = 7c [c is a positive integer] [squaring on both sides ] p2 = 49 c2 --------- (2) Subsitute p2 in equ (1) we get 7q2 = 49 c2 q2 = 7c2 => q is divisible by 7 thus q and p have a common factor 7. there is a contradiction as our assumsion p & q are co prime but it has a common factor. So that √7 is an irrational.

3Thank You

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CBSE > Class 10 > Mathematics