Question

Answer 1

So sánh \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\) và \(\sqrt{3}\)

Bình phương 2 vế: 

VP=3

VT= \(8-2\sqrt{\left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)}=8-2\sqrt{16-7}=8-6=2\) < VP

Vậy  \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\) < \(\sqrt{3}\)

Answer 2

Ta có: \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)

\(=\dfrac{\sqrt{7}+1-\sqrt{7}+1}{\sqrt{2}}\)

\(=\sqrt{2}< \sqrt{3}\)