prove that √5 is a irretional number.
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Let, √5 is a rational number
√5 = p/q [ where p& q are coprime numbers and q is not is equal to 0 ]
squaring both sides
(√5)^2 = (p/q)^2
5 = p^2/q^2
q^2 = p^2/5-----------eq.1
since, p^2 is divisible by 5
therefore, p is also divisible by 5
putting p=5r in eq.1
then, r^2 = q^2/5
therefore q is also divisible by 5
from eq. 1&2 the common factor of p&q is 5 other than 1 so, it is contradiction our assumption is wrong
√5 is an irrational number
H.P
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