1.

Prove that 1 upon 2 plus root 3 is irrational number.

Answer»

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


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