Question

Demonstarati ca nr $\sqrt{3 ^{2n}+3 ^{2n+1} }$,n∈N,este natural

Answer 1

$\sqrt{3^{2n}+3^{2n+1}}= \sqrt{ 3^{2n}*(3+1) }= \sqrt{3^{2n}*4 }= \sqrt{ (3^{n})^{2}*2^{2} }= \sqrt{ (3^{n}*2)^{2} }$$= 3^{n} *2$ ∈ ℕ.