Question

Aratati ca numarul

a=(√3+√5)*(3-√15)+(1-√3)²+4√3 este natural

Answer 1

    
$( \sqrt{3} + \sqrt{5})*(3- \sqrt{15}) +(1- \sqrt{3})^{2}+ 4 \sqrt{3}= \\ (3 \sqrt{3}+3 \sqrt{5}-3\sqrt{5}- 5\sqrt{3}) + (1 - 2 \sqrt{3} +3) + 4\sqrt{3}= \\ -2\sqrt{3}+4 -2\sqrt{3} + 4\sqrt{3} = \\ 4 - 4\sqrt{3}+4\sqrt{3} = 4$