Question

Prove that  1/(2+√3)  is an irrational number.​

Answer 1

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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 contradiction is wrong.

Therefore,1/2+√3 is an irrational number

Answer 2

✨✨Answer is here✨✨

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