Question

prove that √3+ 2 is an irrational​

Answer 1

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Answer 2

Solution :

Let us assume that √3 +2 be a rational number .

Then , it can be expressed as p/q where q ≠ 0 .

√3 + 2 = p/q

Taking 2 on the other side

√3 = p/q -2

Rational number - Rational number = Rational number .

So , p/q - 2 is a rational number .

But this makes our equation wrong that √3 = p/q -2 as √3 is an irrational number .

This contradiction arises due to our earlier supposition that √3 + 2 is rational number . Hence , our supposition was wrong and √3 + 2 is an irrational number.