Question

prove that 2+root 3 is an irrational​

Answer 1

Let 2+√3 is a rational number. A rational number can be written in the form of p/q. p,q are integers then (p-2q)/q is a rational number. ... Therefore,2+√3 is an irrational number.

Step-by-step explanation:

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Answer 2

Answer:

Whole proving in Explanation Panel.

Step-by-step explanation:

Let us assume, the contrary, that 2+√3 is a Rational Number.

Therefore, 2+√3 = a/b , where a and b are co-primes.

2+√3 = a/b

√3 = a/b - 2

√3 = a - 2b/b

Here, a - 2b/b is in the form p/q. So, it is a rational number. Also, √3 is rational.

But, the contradicts fact is √3 is irrational.

So, the contradiction arisen because of our incorrect assumption that 2+√3 is Rational.

Hence, this shows that 2+√3 is irrational.

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