prove that 1 by 2 + root 3 is an irrational number
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Let 1/2+√3 be a rational number.
A rational number can be written in the form of p/q where p,q are integers.
1/2+√3=p/q
√3=p/q-1/2
√3=(2p-q)/2q
p,q are integers then (2p-q)/2q is a rational number.
Then √3 is also a rational number.
But this contradicts the fact that √3 is an irrational number.
So,our supposition is false.
Therefore,1/2+√3 is an irrational number
A rational number can be written in the form of p/q where p,q are integers.
1/2+√3=p/q
√3=p/q-1/2
√3=(2p-q)/2q
p,q are integers then (2p-q)/2q is a rational number.
Then √3 is also a rational number.
But this contradicts the fact that √3 is an irrational number.
So,our supposition is false.
Therefore,1/2+√3 is an irrational number
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