Prove that ?3+?5 is irrational

Let √3+√5 be any rational number x x=√3+√5 squaring both sides x²=(√3+√5)² x²=3+5+2√15 x²=8+2√15 x²-8=2√15 (x²-8)/2=√15 as x is a rational number so x²is also a rational number, 8 and 2 are rational nos. , so √15 must also be a rational number as quotient of two rational numbers is rational but, √15 is an irrational number so we arrive at a contradiction t this shows that our supposition was wrong so √3+√5 is not a rational number Regards