Question

prove that √3 + √5 is irrational
$\sqrt{3} + \sqrt{5}$

Answer 1

${ Hey Dear }$


Here is your answer


Let √3 + √5 is rational


√3 + √5 = P / Q

( √3 + √5 ) ²= ( P / Q) ²


3 + 5 + 2√15 = P² / Q²


√15 = ( P² / Q² - 7 ) 1 / 2



Hence we got RHS is rational and LHS is also rational but √15 is irrational


so, √3 + √5 is irrational


Hence proved