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√7is an irrational number

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√7is an irrational number

Posted by Surendra Singh 5 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Bharti Kumari 5 years, 2 months ago

Underroot7 = a/b [ where a and b are co prime ] 7 = a^2 /b^2 [ squaring both side ] 7b^2 = a^2 ------(1) 7 divides a^2 7divides a Then , a can be written as 2m , where m is an integer . a = 7m 7b^2 = (7m)^2 [ from equation 1] 7b^2 =49m^2 b^2 =7m^2 7 divides b^2 7 divides b Thus, 7 is a common factor of a and b . a and b have no common factor other than 1. Hence , underroot 7 is irrational.

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