Question

Assume ( sqrt{3}+sqrt{2} ) to ( b x ) )ational
So ( sqrt{3}+sqrt{2}=frac{p}{9} )
( z )
( 3+2+2 sqrt{6}=frac{p^{2}}{a^{2}}=5+2 sqrt{6} )
( therefore quad frac{p^{2}-5 q^{2}}{a^{2}}=2 sqrt{6} )
( t )
[
sqrt{b}=frac{p^{2}-5 q^{2}}{2 q^{2}}
]
but RHs is rational
Which is a contradiction.

# 12. Prove that 13+ 2 is irrational.

Solution