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Prove that root 5 be irrational

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Prove that root 5 be irrational

Posted by Ujjwal Pandey 1 year, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Divyanshi Mishra 1 year, 3 months ago

Assume that √5 is a rational number √5=p/q , where p&q are co- prime p=√5q On squaring both sides , we get P^2 =5q^2 (equation 1) P^2 is divisible by 5 P is also divisible by 5 ( by theorem) P=5m From equation 1 =(5m)^2 = 5q^2 = 25m^2= 5q^2 =q^2 =5m q^2 is divisible by 5 q is also divisible by 5 (by theorem) Here we can conclude that p&q both have atleast 5 as a common factor Which contradict our assumption that p&q are co-prime Hence √5 is an irrational number

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