Question

prove that 3+2√2is irrational​

Answer 1

Question:

Prove that 3+2√2 is irrational.

Answer:

Let assume that 3 + 2 √2 is rational. thus it can be written in the form a/b where b is not equal to zero and A and b are coprime.

Therefore,

$= > 3 + 2 \sqrt{2} = \frac{a}{b} \\ \\ = > \frac{3b - a}{b} = \sqrt{2}$

☆since , A and b are integers then we get (3b-a)/b is rational number and √2 is also rational number.

☆but it is not true because √2 is irrational number.

☆therefore the given number 3+√5 is irrational and our assumption taken is wrong.