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Prove root5 is irrational no.

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Prove root5 is irrational no.

Posted by Guru Patel 7 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 7 years, 1 month ago

let √5 be rational
then it must in the form of p/q [q is not equal to 0][p and q are co-prime]
√5=p/q
⇒ √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 = 25× c× 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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