Question

prove that 2+root 3 is an irrational number​

Answer 1

Answer:

Let 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3=p/q

√3=p/q-2

√3=(p-2q)/q

p,q are integers then (p-2q)/q is a rational number.

But this contradicts the fact that √3 is an irrational number.

So,our supposition is false.

Therefore,2+√3 is an irrational number.

Hence proved.

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Answer 2

let us assume that 2+√3 is not an irrational number. then, it will be a rational number. 2+√3= p/q= a/b ( where a and b are co-prime). or, 2+√3 =a/b. or, √3= a/2b. so, an irrational number is not equal to the rational number. so, our assumption was wrong. hence, 2+√3 is an irrational number. i hope it helps you ........