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Prove root 5 is irrational

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Prove root 5 is irrational

Posted by Arjun Arjun 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Shriya Bhattacharya 7 years, 6 months ago

Let us assume that root 5 is rational. Let p and q be real number and co primes. Now, let p and q have another factor other than 1. Now, root 5 = p/q Root 5q= p.....................(i) (Squaring both side) Root 5q whole square = p square 5q square = p square P square is divisible by 5.. Hence, p is divisible by 5.. Let us take p = 5k where k is an integer From eq (i)... P = root 5q 5k = root 5 q (Squaring both side) 25k square = 5q 5k square = q square So, q square is divisible by 5 Hence, q is divisible by 5 Hence, p and q have other factors other than 1, that is 5... Hence our assumption is wrong that p and q are co primes... This contradicts the fact that root 5 is irrational. So, root 5 is irrational.. This sum is looking so lengthy but its actually not..???????

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Posted by Kanika . 1 month ago

CBSE > Class 10 > Mathematics

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Posted by Hari Anand 6 months, 1 week ago

CBSE > Class 10 > Mathematics