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Prove that root5 is a irrational

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Prove that root5 is a irrational

Posted by Riya R 1 year, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Naman Kumar 1 year, 2 months ago

=Let √5 is an rational no. =√5=p/q (where p and q are co-prime no. =√5q=p =on S. B. S. =5q^2=p^2 =q^2=p^2/5 (5 is a factor of p^2. 5 is also a factor of q^2.) =put p=5c =q^2=25c^2/5 =q^2=5c^2 =q^2/5=c^2 (5 is a factor of q^2. 5 is also a factor of q.) =we get 5 is a common factor of p and q. =but p and q are co-prime no. =This is a contradiction. =Our assumption was wrong. = so, √5 is a irrational no. Hence, PROVED

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