Question

Cho em hỏi bài 36 với ạ

Answer 1

1.

\(\frac{3}{\sqrt{5}-\sqrt{2}}-\frac{2}{2-\sqrt{2}}+\frac{1}{\sqrt{3}+\sqrt{2}}\)

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

\(=\frac{3(\sqrt{5}+\sqrt{2})}{3}-\frac{2(2+\sqrt{2})}{2}+\frac{\sqrt{3}-\sqrt{2}}{1}\)

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

 

Answer 2

3.

\(=\frac{5(3+\sqrt{7})}{(3-\sqrt{7})(3+\sqrt{7})}-\frac{2(\sqrt{3}-\sqrt{2})}{(\sqrt{2}+\sqrt{3})(\sqrt{3}-\sqrt{2})}+\frac{-1(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}\)

\(=\frac{5(3+\sqrt{7})}{2}-\frac{2(\sqrt{3}-\sqrt{2})}{1}+\frac{-1(\sqrt{2}+1)}{1}\)

\(=\frac{15}{2}+\frac{5}{2}\sqrt{7}-2\sqrt{3}+2\sqrt{2}-\sqrt{2}-1\)

\(=\frac{13}{2}+\frac{5}{2}\sqrt{7}-2\sqrt{3}+\sqrt{2}\)

Answer 3

5.

\(\frac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{4}{1-\sqrt{7}}=\frac{2(\sqrt{3}-3)}{2(\sqrt{2}-\sqrt{6})}-(\sqrt{3}+1)+\frac{4(\sqrt{7}+1)}{(\sqrt{7}+1)(1-\sqrt{7})}\)

\(=\frac{\sqrt{3}-3}{\sqrt{2}-\sqrt{6}}-(\sqrt{3}+1)+\frac{4(\sqrt{7}+1)}{6}=\frac{\sqrt{3}(1-\sqrt{3})}{\sqrt{2}(1-\sqrt{3})}-\sqrt{3}-1+\frac{2}{3}(\sqrt{7}+1)\)

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

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

Answer 4

7.

\(\sqrt{2}+\frac{1}{\sqrt{5+2\sqrt{6}}}+\frac{2}{\sqrt{8+2\sqrt{15}}}\)

\(=\sqrt{2}+\frac{1}{\sqrt{(\sqrt{2}+\sqrt{3})^2}}+\frac{2}{\sqrt{(\sqrt{3}+\sqrt{5})^2}}\)

\(=\sqrt{2}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{2}{\sqrt{3}+\sqrt{5}}\)

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

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

 

Answer 5

9.

\(=\frac{\sqrt{8}+3}{\sqrt{(\sqrt{9}-\sqrt{8})^2}}+\frac{3+2\sqrt{5}}{\sqrt{(\sqrt{20}-\sqrt{9})^2}}-\frac{1}{\sqrt{(\sqrt{5}+\sqrt{7})^2}}\)

\(=\frac{\sqrt{8}+3}{\sqrt{9}-\sqrt{8}}+\frac{3+2\sqrt{5}}{\sqrt{20}-\sqrt{9}}-\frac{1}{\sqrt{5}+\sqrt{7}}\)

\(=\frac{\sqrt{8}+3}{3-\sqrt{8}}+\frac{3+2\sqrt{5}}{2\sqrt{5}-3}-\frac{1}{\sqrt{5}+\sqrt{7}}\)

\(=\frac{(\sqrt{8}+3)^2}{(3-\sqrt{8})(3+\sqrt{8})}+\frac{(3+2\sqrt{5})^2}{(3+2\sqrt{5})(2\sqrt{5}-3)}-\frac{\sqrt{7}-\sqrt{5}}{(\sqrt{5}+\sqrt{7})(\sqrt{7}-\sqrt{5})}\)

\(=17+12\sqrt{2}+\frac{29+12\sqrt{5}}{11}-\frac{\sqrt{7}-\sqrt{5}}{2}\)

\(=\frac{216}{11}+12\sqrt{2}+\frac{35}{22}\sqrt{5}-\frac{\sqrt{7}}{2}\)