Question

sa se arate ca √mare10+4√6-√mare10-4√6 este numar natural

Answer 1

$\sqrt{10+4 \sqrt{6} }- \sqrt{10-4 \sqrt{6} } = \sqrt{ (\sqrt{6} +2)^2}- \sqrt{( \sqrt{6}-2)^2 }= \\ = \sqrt{6}+2-( \sqrt{6}-2)= \sqrt{6}+2- \sqrt{6}+2=4$∈N