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Prove /5 is irrational

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Prove /5 is irrational

Posted by Santy Kumar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 4 months ago

let root 5 be rational
then it must in the form of p/q [q is not equal to 0][p and q are co-prime]
root 5=p/q
=> root 5 × q = p
squaring on both sides
=> 5×q×q = p×p ------> 1
p×p is divisible by 5
p is divisible by 5
p = 5c [c is a positive integer] [squaring on both sides ]
p×p = 25c×c --------- > 2
sub p×p in 1
5×q×q = 25×c×c
q×q = 5×c×c
=> q is divisble by 5
thus q and p have a common factor 5
there is a contradiction
as our assumsion p &q are co prime but it has a common factor
so √5 is an irrational

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Posted by Kanika . 1 month ago

CBSE > Class 10 > Mathematics