Question

Prove the following number is an Irrational number or not. √3 + 2
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Answer 1

Answer:

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

irrational

√3 + 2 is a irrational number.

Let us consider √3 + 2 as a rational number,

so it can be written as p/q where p and q are integer and q ≠ 0.

Hence

$\sqrt{3} + 2 = \frac{p}{q} \\ = > \sqrt{3} = \frac{p}{q} - 2 \\ = > \sqrt{3} = \frac{p - (2 \times q)}{q} \\ = > \sqrt{3} = \frac{p - 2q}{q}$

Here p-2q / q is a rational number because num. and denom. is integer and q ≠ 0, but we know that √3 is irrational, so our consideration was wrong and √3 + 2 is a irrational number. It has been proved.

hope it helps.