Prove that root 3 is an irrational number. (250 words)
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Prove that root 3 is an irrational number. (250 words)
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Step-by-step explanation:
let us consider that root 3 is an irrational number
two integers a and b such that
root 3 =a÷b
where a and b are coprime.
now
root 3 =a÷b
=(b root3)^2 =a^2 [ squaring both sides ]
= a^2= 3 b^2 ---------------(i)
a square is divisible by 3
a is also divisible by 3
a=3c
(i) = a^2= 3b^2
= (3c)^2 = 3b^2
=9c^2 =3b^2
= b^2 =3c^2
b square is divisible by 3
b is also divisible by 3
but it contradict the fact that a and b are coprime so our considerations is wrong
root is a irrational number.