Question

prove that
$\sqrt{3 + \sqrt{2} }$
is irrational number ​

Answer 1

prove that

$\sqrt{3 + \sqrt{2} }$.........

Answer 2

Sol : Suppose √3 - √2 is rational . Let √3 - √2 = r where r is a rational. ∴ (√3 - √2)2 = r2 ∴ 2 + 3 - 2√6 = r2 ∴√6 = (5 - r2 ) / 2 Now , LHS = √6 is an irrational number . RHS = (5 - r2 ) / 2 But rational number cannot be equal to an irrational. ∴our supposition is wrong. ∴ √3 - √2 is irrational .