Question

prove that root 3 + 2 is an irrational number​

Answer 1

3+√2 = a/b ,where a and b are integers and b is not equal to zero .. therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.. But this contradicts the fact that √2 is irrational.. So, it concludes that 3+√2 is irrational..

Answer 2

Mistake in the question : Prove that 3 + √2 is irrational .

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

So , we can write it in the form p/q .

Hence , 3 +√2 = p/q , where q ≠ 0 .

Taking 3 on the other ,

√2 = p/q - 3

We know that √2 is an irrational number .

This contradicts the fact that it is equal to p/q - 3 , which is a rational number . This proves that our earlier consideration of 3 +√2 as rational is wrong and 3 + √2 is irrational number .