How to proved that √5 is a irrational number...... please explain...... very clearly....!!
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Let us assume that √5 is a rational number.
Then it is of the form a/b.
or, √5= a/b
or, 5 = a^2b^2
or, 5b^2= a^2
or, 5| a^2
or 5| a
now let a= 5c for some integer c
or, a^2= 25c^2
or, 5b^2=25 c^2
or, 5| b
But this is a contradiction.
Hence √5 is an irrational no
Then it is of the form a/b.
or, √5= a/b
or, 5 = a^2b^2
or, 5b^2= a^2
or, 5| a^2
or 5| a
now let a= 5c for some integer c
or, a^2= 25c^2
or, 5b^2=25 c^2
or, 5| b
But this is a contradiction.
Hence √5 is an irrational no
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