Question

Rút gọn:  \(H=\sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}\)

Answer 1

ta có: \(2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}=2.\sqrt{2}.\sqrt{5}+\sqrt{2}.\sqrt{5}.\sqrt{3}-2.\sqrt{2}-\sqrt{2}.\sqrt{3}\)

=>\(\sqrt{2}.\sqrt{5}.\left(2+\sqrt{3}\right)-\sqrt{2}\left(2+\sqrt{3}\right)=\left(2+\sqrt{3}\right).\sqrt{2}.\left(\sqrt{5}-1\right)\)

lại có \(2.\sqrt{10}-2\sqrt{2}=2.\sqrt{2}.\left(\sqrt{5}-1\right)\)

thay vào H ta có : H= \(\frac{2+\sqrt{3}}{2}:\frac{2}{\sqrt{3}-1}=\frac{1+\sqrt{2}}{4}\)

Answer 2

Câu này bằng \(\frac{1}{2}\) cơ Nguyễn Văn An