Find the value of root 5 is irrational?
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let us assume to the contrary that root 5 be a rational number.
say a/b, where a nd b are integers and coprimes.
root 5 = a/b
squarying, (root 5)2= (a/b)2
5= a2/b2
5b2=a2 ----------------(i)
5 divides a2
therefore, 5 divides a-----------(ii)
let a=5c for some integer c
substitute 'a' in (i)
5b2=(5c)2
5b2= 25c2
b2= 5c2
therefore, 5 divides b---------(iii)
from (ii) nd (iii) it is proved that 5 divides a nd b which is a contradiction to a nd b are c0-primes. this contradiction has occurred due to our incorrect assumption that root 5 is rational.
hence proved that root 5 is irrational.
say a/b, where a nd b are integers and coprimes.
root 5 = a/b
squarying, (root 5)2= (a/b)2
5= a2/b2
5b2=a2 ----------------(i)
5 divides a2
therefore, 5 divides a-----------(ii)
let a=5c for some integer c
substitute 'a' in (i)
5b2=(5c)2
5b2= 25c2
b2= 5c2
therefore, 5 divides b---------(iii)
from (ii) nd (iii) it is proved that 5 divides a nd b which is a contradiction to a nd b are c0-primes. this contradiction has occurred due to our incorrect assumption that root 5 is rational.
hence proved that root 5 is irrational.
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