Question

Prove that √2 + √3 is an Irrational number .

Answer 1

root 2 +root 3 =p/q

square on both sides

2square +3 square+2×root2×root3 =[p/q]2

4+9+ 2root6=(p/q)2

13 +2root6 =(p/q)2

2root 6 = p square +13q square/q square

root6=p square +13q square/2q square

wkt root 6 is an irrational number

p square +13q square/2q square is an rational number

root2+root3 is an irrational number