* \(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-\frac{6\sqrt{2}-4}{3-\sqrt{2}}\)\(=\frac{\left(\sqrt{8}-\sqrt{7}\right)}{\left(\sqrt{8}+\sqrt{7}\right)\left(\sqrt{8}-\sqrt{7}\right)}+\sqrt{25.7}-\frac{2\sqrt{2}\left(3-\sqrt{2}\right)}{3-\sqrt{2}}\)

\(=\sqrt{8}-\sqrt{7}+5\sqrt{7}-2\sqrt{2}=2\sqrt{2}+4\sqrt{7}-2\sqrt{2}=4\sqrt{7}\)

** \(\frac{\sqrt{6-\sqrt{11}}}{\sqrt{22}-\sqrt{2}}+\frac{6}{\sqrt{2}}-\frac{3}{\sqrt{2}+1}\)\(=\frac{\sqrt{2}\sqrt{6-\sqrt{11}}}{\sqrt{2}\left(\sqrt{22}-\sqrt{2}\right)}+\frac{6\sqrt{2}}{2}-\frac{3\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}\)

\(=\frac{\sqrt{12-2\sqrt{11}}}{2\sqrt{11}-2}+3\sqrt{2}-\frac{3\sqrt{2}-3}{1}\)\(=\frac{\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}+1^2}}{2\left(\sqrt{11}-1\right)}+3\sqrt{2}-3\sqrt{2}+3\)

\(=\frac{\sqrt{11}-1}{2\left(\sqrt{11}-1\right)}+3=\frac{1}{2}+3=\frac{7}{2}\).

Cảm ơn bạn :)

\(=\frac{1}{2}+3\sqrt{2}--3+3\sqrt{2}\)

\(=\frac{1+6\sqrt{2}}{2}--3+3\sqrt{2}\)

\(=\frac{-5+12\sqrt{2}}{2}\)

KÉO XUỐNG SẼ CÓ ĐÁP ÁN

Tò mò thì kéo đi

Phê3

tiếp đi

..............................

HẾT

\(\frac{\sqrt{12-2\sqrt{11}}}{2\left(\sqrt{11}-1\right)}+3\sqrt{2}-3\left(\sqrt{2}-1\right)\)

\(=\frac{\sqrt{\left(\sqrt{11}-1\right)^2}}{2\left(\sqrt{11}-1\right)}+3\sqrt{2}-3\sqrt{2}+3\)

\(=\frac{1}{2}+3=\frac{7}{2}\)

Ghi rõ đề ra đi bn

Đề là Tính ă bạn

a. \(\sqrt{50}-\sqrt{3}.\sqrt{6}+\frac{\sqrt{22}}{\sqrt{11}}=5\sqrt{2}-3\sqrt{2}+\sqrt{2}=3\sqrt{2}\)

b. \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\sqrt{7+4\sqrt{3}}=\frac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\frac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-\sqrt{\left(2+\sqrt{3}\right)^2}\)

\(=\sqrt{3}+2+\sqrt{2}-2-\sqrt{3}=\sqrt{2}\)

a) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)

\(=\left(\sqrt{9\cdot11}-\sqrt{9\cdot2}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)

\(=\left(3\sqrt{11}-3\sqrt{2}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)

\(=3\cdot11-3\sqrt{22}-11+3\sqrt{22}\)

\(=33-11=22\)

b)\(3\sqrt{\frac{9}{8}}-\sqrt{\frac{49}{2}}+\sqrt{\frac{25}{18}}\)

\(=\frac{9}{\sqrt{8}}-\frac{7}{\sqrt{2}}+\frac{5}{\sqrt{18}}\)

\(=\frac{9}{2\sqrt{2}}-\frac{7}{\sqrt{2}}+\frac{5}{3\sqrt{2}}\)

\(=\frac{27-42+10}{6\sqrt{2}}\)

\(=-\frac{5}{6\sqrt{2}}\)

c)\(\left(1+\frac{5-\sqrt{5}}{1-\sqrt{5}}\right)\left(\frac{5+\sqrt{5}}{1+\sqrt{5}}+1\right)\)

\(=\left(1-\frac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}\right)\left(\frac{\sqrt{5}\left(\sqrt{5}+1\right)}{1+\sqrt{5}}+1\right)\)

\(=\left(1-\sqrt{5}\right)\left(\sqrt{5}+1\right)\)

\(=1-5=-4\)

 

B=\(\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3\sqrt{3}+3}{\sqrt{3}+1}=\frac{6\left(1-\sqrt{3}\right)}{1-\sqrt{3}}+\frac{3\left(\sqrt{3}+1\right)}{\sqrt{3}+1}=6+3=9\)

C=\(\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}=\frac{3\left(1+\sqrt{3}\right)}{\sqrt{3}}+\frac{\sqrt{3}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}=\sqrt{3}+1-\sqrt{3}=1\)

D=\(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}=\frac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)

E=\(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\frac{1}{2-\sqrt{3}}=\frac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}+\frac{1}{2-\sqrt{3}}=\sqrt{3}+\frac{1}{2-\sqrt{3}}=\frac{2\sqrt{3}-1}{2-\sqrt{3}}\)