= \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\) ( vì căn 16 = 4)
=\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\) (vì căn 4 = 2 mà 2 + 2 = 4 nên tách luôn thành căn 4 )
= \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
= \(\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1+\sqrt{2}\)
Đúng nha lần sau mình giải tiếp cho
(\(3\sqrt{2}\)+\(\sqrt{6}\))\(\sqrt{6-3\sqrt{2}}\)
\(\frac{\sqrt{5}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{4}+\sqrt{4}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}\)
\(=\frac{\left[\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{6}+\sqrt{8}+\sqrt{4}\right)\right]}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}\)
\(=\frac{\left[\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{2}.\sqrt{3}+\sqrt{2}.\sqrt{4}+\sqrt{2}.\sqrt{2}\right)\right]}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}\)
\(=\frac{\left[\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right).\sqrt{2}\right]}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}\)
\(=\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}\)
\(=1+\sqrt{2}\)