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\(B=\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}=\frac{9\sqrt{5}+9\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{9\left(\sqrt{5}+\sqrt{3}\right)}{\sqrt{5}+\sqrt{3}}=9\)
\(C=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{4}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\sqrt{2}+1\)
mik chỉnh lại đề
\(D=\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}=\frac{6\sqrt{2}-4\sqrt{3}+2\sqrt{5}}{9\sqrt{2}-6\sqrt{3}+3\sqrt{5}}\)
\(=\frac{2\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}{3\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}=\frac{2}{3}\)
a) \(=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{16-2.4\sqrt{2}+2}}}\)
\(=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{\left(4-\sqrt{2}\right)^2}}}=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+4-\sqrt{2}}}\)\(=\sqrt{6-2\sqrt{3+2\sqrt{3}+1}=\sqrt{6-2\sqrt{\left(\sqrt{3}+1\right)^2}}=\sqrt{6-2\left(1+\sqrt{3}\right)}}\)
\(=\sqrt{\left(\sqrt{3}+1\right)^2}=1+\sqrt{3}\)
b) Tương tự a) đ/s =5
\(\frac{4+\sqrt{2}-\sqrt{3}-\sqrt{6}+\sqrt{8}}{2+\sqrt{2}-\sqrt{3}}\)
\(=\frac{\left(\sqrt{4}+\sqrt{2}\right)-\left(\sqrt{3}+\sqrt{6}\right)+\left(\sqrt{4}+\sqrt{8}\right)}{2+\sqrt{2}-\sqrt{3}}\) ( Tách 4 thành \(\sqrt{4}+\sqrt{4}\) )
\(=\frac{\sqrt{2}\left(\sqrt{2}+1\right)-\sqrt{3}\left(1+\sqrt{2}\right)+\sqrt{4}\left(1+\sqrt{2}\right)}{2+\sqrt{2}-\sqrt{3}}\)
\(=\frac{\left(\sqrt{2}-\sqrt{3}+2\right)\left(\sqrt{2}+1\right)}{2+\sqrt{2}-\sqrt{3}}\)
\(=\sqrt{2}+1\)
\(N=\sqrt{4\sqrt{6}+8\sqrt{3}+4\sqrt{2}+18}\)
\(N=\sqrt{12+4+2+2\cdot2\sqrt{3}\cdot\sqrt{2}+2\cdot2\sqrt{3}\cdot2+2\cdot2\cdot\sqrt{2}}\)
\(N=\sqrt{\left(2\sqrt{3}\right)^2+2^2+\left(\sqrt{2}\right)^2+2\cdot2\sqrt{3}\cdot\sqrt{2}+2\cdot2\sqrt{3}\cdot2+2\cdot2\cdot\sqrt{2}}\)
\(N=\sqrt{\left(2\sqrt{3}+2+\sqrt{2}\right)^2}\)
\(N=2+2\sqrt{3}+\sqrt{2}\)