Question

[maionline]

so sanh \(\sqrt{5}+\sqrt{7}\) va 2\(\sqrt{6}\)

giai full giup minh nhe!thanks

Answer 1

[Nguyễn Quỳnh]

Ta có : \(\left(\sqrt{5}+\sqrt{7}\right)^2=5+7+2\sqrt{35}\)

=\(12+2\sqrt{35}\le12+2\sqrt{36}=12+2.6=24\)

Mà \(\left(2\sqrt{6}\right)^2=24\)

Do đó \(\left(\sqrt{5}+\sqrt{7}\right)^2< \left(2\sqrt{6}\right)^2\)

Mà \(\sqrt{5}+\sqrt{7}>0\) và \(2\sqrt{6}>0\)

Vậy \(\sqrt{5}+\sqrt{7}< 2\sqrt{6}\)